This is such a common thing I think for first baby couples. Assuming he is not a total twat like shimmery's ex was (well done you by the way for kicking him out by the way!!) then some men just don't 'get it'.
And us women have a tendency to seethe inwardly rather than just saying what we want. My DH was utterly, totally, selfish and lazy when we had our first DD. Out on the piss after work during the week, sleeping on the sofa all weekend. I'm amazed I didn't cut his knackers off at some point. 
BUT here we are, 2 DCs later and he is a very unselfish, hard-working hands-on dad. He still needs a nudge every now and again (during the Grand Prix for example!) but we try to give each other some time off or a sleep in and just share the rest.
It's taken rows, tears, rational conversations, more rows/tears etc.. but eventually he got it.
The problem is men assume we'll tell them whenever we want them to do something. They prefer it that way because then they don't have to think AND the default is that they do nothing until asked. Then when you ask you feel like you're nagging, or they tell you you're nagging!
I agree with the posters on here who have said to spell it out in a list or rota. Agree on weekend sharing of chores/baby jobs/whatever. If you're on meds you need support and sleep and he needs to pull his finger out.
It may take some time but hang in there. My doc once said to me "if you collapse, then everything collapses with you. Move yourself up a bit on your list of priorities" which I thought was pretty good advice.
Best of luck to you! 