Wearing a wool clothing on top of a linen clothing or vice versa:[1]

It is permitted to wear a wool shirt on top of a linen shirt [or vice versa].

Tying them together:[2] It is even permitted to tie the two clothing together in a way that they cannot be removed without first untying the knot. Furthermore, even if the knot is a permanent knot it is permitted. It is only forbidden if the clothing is attached through the stitch of a thread.[3] However, there are opinions[4] who prohibit making a permanent knot.^[5] [Practically, the worldly custom is to be lenient in the above like the former opinion.[6] However some Poskim[7] learn that the entire dispute above is referring to using an external string, such as a belt, to attach the two clothing to each, however to attach the clothing to each other in a permanent knot is forbidden according to all.]

Wearing in a way that the lower clothing cannot be removed without first removing the upper clothing:[8] Some Poskim[9] rule it is forbidden to wear linen pants^[10] [or socks[11]] over wool pants or vice versa, being that one cannot remove the lower pants without removing also the upper pants with it[12], and it is thus considered like an attachment of wool and linen. [The same applies by any clothing worn in a way that the lower one cannot be removed unless one first removes the upper one.] Shirts however may be worn one over the other as one can remove the lower shirt without removing the upper shirt.^[13] [However, other Poskim[14] rule it is permitted to wear two pants over each other even though one is unable to remove the lower one without first removing the upper one.] Practically, its proper for one to be careful [and avoid wearing wool and linen pants over each other].^[15] [However the custom is to be lenient in all the above.[16]]

Linen Belt/elastic on wool garment:[17] It is permitted to wear a linen belt/string, or linen elastic, over a wool pants or vice versa. It is even permitted to insert the belt/string into the material of the pants for use of tightening the pants [as is common in sweat pants and hoods[18]] so long as it is possible to remove the string without needing to cut the sewing.[19] It is even permitted to make a single knot with the string upon wearing it. One however may not make a double knot on the string.[20] [It goes without saying that it is forbidden to attach the belt in a way that it cannot be removed unless one cuts the sewed material. However, the custom is to be lenient in all the above[21] so long as the belt is not sewed onto the pants.]   

Belt over two garments, one of wool and other of linen:[22] Some Poskim[23] rule that [according to the stringent opinion brought above], it is forbidden to wear a belt over two pairs of clothing, one wool and the other linen. Other Poskim[24] rule it is permitted to wear a belt over the two clothing and so is the practical custom of all Jewry.

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[1] Michaber Y.D. 300:4; Tur 300; Rambam Kilayim 10:11; Rosh Nida 20; Tosefta Kilayim 5:10; Rabbeinu Yerucham Nesiv 19; For proper background on this Halacha, see Beis Yosef 300

[2] Michaber ibid; Poskim ibid

Background: The Halacha here is dealing with tying wool and linen to each other, and whether it is permitted to do so even with a permanent knot. It is unclear from Michaber, and seemingly disputed, as to the technicalities of the case; is it referring to a case that one is tying the clothing to each other, or is it referring to a case that one is using a string/belt to tie them together? The Taz 300:9 and Aruch Hashulchan 300:22 learn like the later approach and hence rule that to tie them to each other with a permanent knot is forbidden according to all. However, from the Shach 300:7 and Beir Hagoleh it seems they learn the dispute is even in a case that one is tying the clothing to each other. Vetzaruch Iyun!

[3] Michaber ibid; Beis Yosef 300 based on Rashba 3:226 that a knot is not considered an attachment in regards to the prohibition of Kilayim; See however Shach 300:7 who states the understanding of the Michaber in the Rashba ibid can be argued.

[4] Tur 300 in name of Rosh in understanding of Tosefta Kilayim; However, see Taz 300:9 who says this is the opinion of Rabbeinu Yona mentioned in Beis Yosef 300; See Aruch Hashulchan 300:22 who learns like Taz ibid although severely questions the existence of this opinion

^[5] Michaber ibid; According to this opinion it would likewise be forbidden to place a belt over a wool pants and linen shirt or vice versa, however the world has already been accustomed to permit using a belt in such situations, as is mentioned by the Rashba ibid. [Taz 300:9]

[6] Shach 300:8; Levush, brought in Taz 300:10; Aruch Hashulchan 300:24

[7] Taz 300:9 in explanation of Michaber ibid that the entire Halacha here is dealing with tying the two clothing together using an external belt as to tie them to each other in a permanent knot “why should it be permitted”; So rules Tur 300 in name of Rosh based on Tosefta 5:10; See Aruch Hashulchan 300:20-22

Other opinions: From the Shach 300:7 and Beir Hagoleh it seems they learn the dispute is even in a case that one is tying the clothing to each other. Vetzaruch Iyun!

[8] Rama 300:4

[9] Rama’s understanding of Hagahos Ashri Beitza; Beis Yosef in name of Yerushalmi Kilayim 4; This opinion in Rama is going according to the latter, stringent, opinion mentioned in Michaber ibid who prohibits making a double knot. [Shach 300:8]

Other opinions: Some Poskim rule that even according to the stringent opinion, it is only forbidden if one cannot remove the upper garment without the lower garment. [Beis Yosef 300 in explanation of Yerushalmi, brought in Taz ibid] Some Poskim severely question the existence of this opinion brought by Rama saying it is a misunderstanding of Hagahos Ashri and has nothing to do with the opinion of the Tur ibid who prohibits tying items together in a permanent knot. [Maharsham 3:292; Aruch Hashulchan 300:22; See Chelkas Yaakov 3:172]

^[10] Bateiy Shukayim

[11] Shach 300:9; Nussach in Hagahos Ashri ibid, brought in Beis Yosef 300

[12] See Taz 300:10 that this refers to pants that cover the feet.

^[13] Rama ibid; See Shach 300:10 and Taz 300:10 for explanation; See Chelkas Yaakov 3:172

Other opinions: Some Poskim rule it is forbidden to wear two shirts one over the other if one is wool and the other is linen, as one cannot remove the lower shirt without first removing the upper one. [Levush, brought in Shach 300:10 and Taz 300:10] Shach ibid argues on the Levush saying that by a shirt one doesn’t have to completely remove the upper one in order to remove the lower one, as he can slip his arms out of the sleeves of both shirts and then remove the lower shirt while the upper shirt still remains on his body, and therefore it is not considered Shatnez. Taz ibid gives a similar explanation in defense of Rama against Levush, however says that anytime that the upper clothing is removed even partially it is considered Kilayim.

[14] Shach 300:8 that the first opinion in Michaber ibid argues on this opinion brought in Rama ibid; Beir Hagoleh in name of Beis Yosef and Maharshal that majority of Poskim follow the opinion of Rebbe Yossi who rules there is never Kilayim unless sewed

^[15] Rama ibid; Taz 300:10 rules like the stringent opinion; Shlah p. 106a, brought in Pischeiy Teshuvah 300:6; See Chelkas Yaakov 3:172

[16] Shach 300:8; Levush, brought in Taz ibid; Aruch Hashulchan 300:24, see there in length

The reason: The world is accustomed to be lenient in the above like the first opinion mentioned in Michaber ibid. [Shach ibid]

[17] Rama 300:4

[18] Rama ibid “The string goes from one side to the other similar to the leather strap in the Tefillin that goes through the Mabarta.”

[19] The reason: As since one is able to remove the belt:elastic without needing to udo the sewing it is similar to wearing a linen belt on a wool garment. [Rama ibid]

[20] The reason: As since one is not able to remove the belt:elastic without undoing the knot [it is therefore considered attached]. [Rama ibid]

[21] Shach 300:8

The reason: The above ruling is only according to the stringent opinion mentioned by the Michaber in the previous law. Practically the world is accustomed to be lenient in the above like the first opinion mentioned in Michaber ibid. [Shach ibid]

[22] Taz 300:9

[23] Rabbeinu Yona, brought in Beis Yosef 300 and Rashba and Taz ibid; Taz ibid explains that this is the intent of the Michaber ibid in his second opinion

[24] Taz 300:9 based on Rashba that so is custom of all Jewry; Tosefta brought in Taz ibid; Aruch Hashulchan 300:22

[25] Michaber and Rama 300:4; Rambam; Rosh; Tosefta

[26] The reason: As the two garments are not attached in any way, and one can remove one without removing the other, thus being permitted according to all. [See Rama ibid; Taz 300:8-9]