Listening to one’s wife sing:
While Davening or learning Torah: The singing voice of a woman is [Rabbinically] an Erva. This applies whether she is single or married, and even towards the voice of one’s own wife [even while she is pure]. Thus, it is [Rabbinically] forbidden for a husband to recite Kerias Shema, or Daven, or recite words of Torah, while hearing his wife sing. Nonetheless, if one is able to concentrate on his prayer to the point that he does not even consciously hear or pay attention to her voice, then it is permitted [to learn and Daven while hearing it].
Wife is pure-not Davening/Learning: It is permitted for a husband to hear his wife sing during non-Nida times, if he is not involved in Torah learning or Davening.
May a wife sing a lullaby to soothe her baby to sleep if her husband is around?
A woman during Nida times is to beware not to sing lullabies to her child if her husband is around. However, if the baby is crying and cannot be soothed in another manner, then she may do so even during Nida times. However, if possible, the husband should leave the room or close his ears in order to avoid hearing her sing. During non-Nida times, it is completely permitted so long as the husband is not in the midst of Torah learning or Davening.
May a wife sing Zemiros together with her husband on the Shabbos table?
It is forbidden for one’s wife to sing Shabbos Zemiros during times of Nida. This applies even if she is singing together with other family members or guests. During times of purity, however, it is permitted for her to do so [if other male guests are not present]. Nonetheless, some limit this only to tunes that do not contain verses of scripture or the name of Hashem.
May a husband listen to his wife play a musical instrument?
Yes. However, some Poskim rule that a husband may not listen to his wife playing musical instruments during Nida times if she is doing so on his behalf.
 Admur 75:6; Michaber O.C. 75:3 and E.H. 21:1; Yireim 392; Rabbeinu Yona Brachos 25b
 Nishmas Adam 4:1; Kaf Hachaim 75:27; However, see Michaber ibid; Perisha 21:2 on Tur E.H. 21 who rules that listening to the singing of an Erva is Biblically forbidden.
 Admur 75:6; Michaber O.C. 75:3 and E.H. 21:1; Shmuel in Brachos 24a “The voice of a woman is an Erva”
The reason: This is learned from a verse in Shir Hashirim that states “Ki Kolecha Areiv:Because your voice is pleasant.” [Brachos ibid] From here we learn that the voice of a woman is attractive and contains a lust. [Rashi ibid]
 Admur ibid; M”A 75:6; Beis Shmuel E.H. 21:6 [regarding prayer]; Bear Sheva, brought in Beir Heiytiv 21:4 [regarding anytime]; Beis Oved 17; Chesed Lealafim 75:6; Ben Ish Chaiy Bo 13; Kaf Hachaim 75:21
Other opinions: Some Poskim rule that al
 Admur ibid; Rama 75:3; Ohel Moed 5:5; Hagahos Maimanis
 Pashut; Piskeiy Teshuvos 75 footnote 106
 Nishmas Adam 4:1; Kaf Hachaim 75:27
 Forbidden or only Lechatchila should avoid? Some Poskim rule it is forbidden from the letter of the law. [Darkei Moshe 75:3] Other Poskim rule that it is merely initially to be avoided. [Michaber ibid; Beis Yosef 75 “Proper to be careful”; P”M 75 A”A 6 writes the Rama in 75:3 rules like the Michaber, unlike his ruling in Darkei Moshe; Kaf Hachaim 75:25] Admur ibid rules like the Darkei Moshe that it is forbidden. The practical ramification is in a case of Bedeived, that one Davened while hearing her voice, and whether one must repeat the prayer. [P”M 75 A”A 6]
 Admur 75/6 “Forbidden”; Michaber O.C. 75:3 regarding women in general “Beware”; Rama 75:3 regarding wife; Ohel Moed 5:5 regarding wife; Hagahos Maimanis regarding wife; Beis Shmuel E.H. 21:4 “Forbidden”; Rabbeinu Yona ibid regarding Davening; Yireim 392 and Mordechai Brachos Remez 80 regarding learning.
 Admur ibid; Olas Tamid 75:5; Rabbeinu Yona ibid; Kitzur SHU”A 5:16; Kaf Hachaim 75:26; See Beis Yosef 76
 Pischeiy Teshuvah 195:10; Kitzur SH”A 153:10; Lechem Visimla 195:20; Ben Ish Chaiy Tzav 2:25; Igros Moshe 2:75; Kitzur Dinei Taharah 3:3; Shiureiy Sheivet Halevi p. 264; Sheivet Halevi 5:176; Taharah Kehalacha 14:24
Other opinions: Some Poskim rule that the prohibition of Kol Isha does not apply towards one’s wife, as the entire reason for the prohibition is so one not come to look at her, and it is permitted to look at one’s wife even during Nuda times. [Suga Beshoshanim 95:2; Mishnas Yaakov 3:117; Chemdas Moshe 58, brought and explained in Taharah Kehalacha 14 footnote 58]
 Beir Sheva p. 119, brought in Kaf Hachaim 75:23; Elya Raba 75:5; Shaar Hatziyon 560:25; Piskeiy Teshuvos 75:12
 Ben Ish Chaiy Tzav 2:25; Tahrah Kehalacha 14:25
 See Chok Yaakov 479:6 that a woman should not sing the Hodu by Halel of the Seder due to Kol Isha; Yosef Ometz 603; Be’r Sheva Kuntrus Ber Mayim Chaim 3; Az Nidbaru 3:71; 9:59; Otzer Haposkim 21; Menachem Meishiv 26; Tahrah Kehalacha 14:24; Halichos Bas Yisrael 6:11
 Be’r Sheva Kuntrus Ber Mayim Chaim 3; Be’r Yehuda on Sefer Chassidim L.S. 3; Suga Beshoshanim 16:6-7; Shevet Halevi 5:197-4; Shiureiy Shevet Halevi 6:2; Taharah Kehalacha 14:24; Halichos Bas Yisrael 6:11
Other opinions: Some Poskim argue and rule the prohibition of Kol Isha does not apply when a group of people are singing together. [Chasam Sofer O.C. Shaar Taharas Hayadayim 14 based on Shoftim 5 that Devora and Barak sang together the Shira; See also Sridei Aish 2:8 regarding Zemiros]
 Implication of Chok Yaakov and Poskim ibid that the singing of Zemiros is not considered Torah learning even though it contains words of verses. Vetzaruch Iyun!
 Halichos Bas Yisrael 6:11
 Minchas Yitzchak 7:70; brought in Tahrah Kehalacha 14:24