Assalamu'alaikum w.w.
Some scholars consider this to be against the Islamic principles of modesty as it involves the husband being present infront of midwifes while the wife is in a state of undress. In Western countries however, female relatives are not always readily available to accompany a woman to the delivery unit, especially during night hours. With this in mind, I consider it permissible for the husband to be present during the wife's labour.

Allah (SWT) Knows Best.
(Mufti) Abdullah Patel.