My DS is only 6 weeks so early days but so far (he is bottle fed with expressed breast milk for medical reasons so that affects things):
For the first week or so, I had to do a lot of pumping in the night to get my supply established and I was also physically recovering from a difficult birth - my DH did 90% of the night feeds (but, as I say, I was also up in the night pumping so I think this was really more 50:50)
For weeks 2-3, I was able to pump a lot less often so we switched to a shift system - usually, my DH did 8pm-midnight/1am, I did the rest.
Weeks 4 - now, my DH does 10pm-2am, I do the rest. Friday night is my night completely off, I go and sleep in the spare room and Sunday night is my DH's night completely off.
If my DS's naps in the day become more regular and I can nap more during the day - currently, given the need for me to express and wash and sterilise bottles, plus a 6 week old who is naturally still erratic in feeding/sleeping, I haven't managed to nap at all during the day - I'd like to be able to get my DH a bit more sleep, as he does have a lot of work on at the moment.
I am always stunned by reading mumsnet at the number of men who do very little/nothing and the women who put up with it.