Call me old fashioned, but if you are on maternity leave and Your DH is at work he should never be expected to wake up early/in the night with his DC.
Yep, you're old fashioned! 
OP, if you're doing all the night feds/wakes, then I think it's fair enough asking your dh to get up with the baby at 5.45am or whenever the baby wakes.
Urgh, I think women who expect their FT working partner to do and equal share of ‘night stuff’ whilst they themselves are on maternity leave, are THE WORST!!
Meteor, OP is not asking her dh to do 'an equal share'. She's asking him to get up early some days with the baby, not do night wakings. She has not said he's a surgeon or anything like that...
Im normally cooking tea doing washing tidying up for a while etc but try being settled in bed by 9 at latest
OP, what's your h doing while you're doing this?