Equal 'down time' is the way to go.
When he is at work or commuting, you work, either in your job, or looking after the baby, or doing housework.
When he comes home and sits on the sofa, you sit beside him.
Don't get up.
If the baby needs something, get up to fetch it, then sit back down with the baby.
When he says "what's for dinner?", you say, "I don't know, shall we go and make something?" Then don't get up off the sofa until he does.
If he goes out for an evening, monitor the hours he is out of the house, and within 2or 3 days you go out for the same number of hours, leaving the baby with him (even if you have nowhere to go but a café or pub alone - go and read a book).
You will probably find that the housework slips, stuff is not done, etc.
Hold firm, don't cave in.
When he (finally, eventually) notices and complains about the state of the place, say "Why don't you clean the bathroom while I tackle the sitting room?"
Again, don't start actually doing the cleaning until he starts.
When he complains that he can't find his clothes, or has no clean clothes, don't react. Say in a pleasant voice "why don't you put a wash on while I tidy up the baby toys".