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

nope. in fact, if your hubby isn't home the entire day and you take care of the baby alone, it is important he takes care of the baby at least for some time in the night, so that you can get some time to rest or do things that can help you relax. tell him to use the time to play with the baby and develop a bond. the more you let him do it the more he will finally do. i don't mean he should take care of the baby through the whole night, but a couple of hours should be enough for you to rest too, if not more.