Is it too much to expect my husband to look after the baby when she cries in night time?

Absolutely not. Rather, being the father or being the person in the room, he should be anyway helping you with chores of the baby. I do understand that if your husband is working and has to go to office, it is not right to keep him awake most of the nights, but yes, patting and pacifying the baby for sometime is not a big deal. And that goes for a working mom as well.