What is the reference in the scene where the husband jokes about naming children?
This pose is typical for Gendo Ikari from the Evangelion series. It even has a page on knowyourmeme and is also featured as an example for 'Finger Tenting' on tvtropes.



In the series he has a son named Shinji and daughter (sort of) named Rei.
(The reference right afterwards is also to Evangelion's Kaworu)