Funny one this in our household, DP was more than happy to help at night even though I bf (I would express during the day to have a feed for night wake so DP could do if he wanted). We had a general rule that i would do two thirds whilst on mat leave and then we would do one day each at weekend, when I went back to work we did a week each as then at least we were both well rested for a week at a time (in theory). Of course there always had to be flexibility if one of us had an important day at work or a particularly early start.
I found though, that I couldn't sleep if DS was stirring even if DP was happy to do the feed so would end up taking over... tbh I think he would get quite upset about that as he wanted to do more!
Although I am happy to admit I am a massive control freak
I do think it was me more than DP who was the problem during this early night waking stage.
Ah, well, I don't think there is a right answer, it is just whatever feels comfortable for you, but, if you do want more help, then I would suggest asking and if you don't get it, kick up a fuss.
I always found that lack of dinner when he arrived from work, because I was too busy with DS, prompted DP to get the message quite nicely!
DP still pretty hands on and DS 2 next week, so think I am one of the lucky ones...