Chiyuv for Aliyah-The custom for a husband to get an Aliyah after birth:

Shabbos before Bris:[1] The father of a newborn male child is considered a Chiyuv on the Shabbos before the Mila [or Shabbos of the Mila, if he has not yet received an Aliyah after the birth[2]].

Wife coming to Shul:[3] The father of a newborn son or daughter, or even a stillborn, is considered a Chiyuv on the first Shabbos that his wife comes to Shul after birth.[4] If she has not yet come to Shul, then on the 40th day for a boy, and 80th day for a girl, he is considered a Chiyuv. One’s whose wife has a miscarriage of a recognizable fetus, is also considered a Chiyuv.[5] [The above Chiyuv applied only in previous times when it was customary for the wife to not leave the house until she is healthy, in which case her first stop would be to the Shul. However today, this custom of having the wife make her first visit after birth be to a Shul is no longer practiced, and hence this Chiyuv is no longer relevant.[6]]

Naming daughter:[7] The father is to get an Aliyah on the day of the naming of his daughter. Some Poskim[8] learn that he is considered a Chiyuv. Other Poskim[9], however, learn that he is not considered a Chiyuv, although the custom is to give him an Aliyah.

[1] See Piskeiy Teshuvos 136:9

[2] Piskeiy Teshuvos ibid

[3] M”A 282 in end; Elya Raba 219:5; Migdal Oz of Yaavetz; Shaareiy Efraim 4:28; Tosefes Shabbos 282:15; Bigdei Yesha 218:12; Daas Torah 282; Kitzur SHU”A 78:11; Hisorerus Tehsuvah 99; Biur Halacha ibid; See Piskeiy Teshuvos 136:8; Poskim in Nitei Gavriel 69:1-24 and Poskim in footnote 1; Toras Hayoledes 69:8

[4] See above that the wife would come to shul after four weeks from birth.

The reason: A woman who gave birth needs to bring a Karban. Today, during exile, the above practice was instituted in the place of the Karban, through her husband receiving an Aliyah to the Torah upon her return to the outside. [See M”A 282:18; Poskim ibid; Nitei Gavriel 69:1 footnote 1-2]

[5] Biur Halacha ibid

[6] See Piskeiy Teshuvos 136:8

[7] See Shevach Habris 21:1 footnote 2

[8] M”A 282 in end that the father of a newborn daughter comes before the father of a newborn son; Daas Torah on M”A ibid

[9] Machatzis Hashekel 282 on M”A ibid; Tosefes Chaim on Chayeh Adam 31:22; Minchas Yitzchak 4:107; Piskeiy Teshuvos 136:10;