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

Not at all, because he also played a part in the conceiving part and it is his daddy responsibility to take care of the child too. Then again, I remember my hubby ever reminded me that while I tended to my baby during the day, he was out working hard for the family too. So he also needed his rest. Perhaps can talk to your hubby in a gentle tone and suggest taking turns instead. I think our hubbies will be more receptive to a loving suggestion rather than a demanding one. All the best!