My husband saved my life when I passed out after losing too much blood after the delivery and by some inexplicable circumstance no one except him was in the room and the nurses were at the far end of the corridor. The call button was not at the head of the bed as it was supposed to be, but hidden away in a drawer.
OP,
In this day and age, it's expected that a father would witness the birth of his children. If he can't handle the blood and moaning, then he shouldn't have copulated and doesn't deserve the babies.
PP, there are many things that a husband can do for their partner when she is giving birth! Psychologically, the very fact that you are there (not passing out) is a symbol of your engagement. If you utter words of encouragement and hold her hand, even better. If you cut the cord, hold your baby, etc even better.