Hmm, I think both of you ABU and ANBU in different ways.
He seems to be incredibly unsupportive of your post CS recovery, that's a real problem. Was he like this after having your first two children?
He is also being unreasonable to claim that he wants weekends free for family leisure time, if he is not offering you equal opportunity to jump into your hobbies or spend time away from the children as he seems to.
I hesitate to say you are being unreasonable, because it seems like he isn't pulling his weight domestically. This is the major issue that needs to be resolved, which I think would incentivise you to do what you can to give you both weekends off from housework.
I don't discount the stress of working long days for someone else, so I also feel for him somewhat. Those hours are wearing, the job may also be demanding and there is a lot of pressure knowing that your salary is looking after five people who all depend on you. I don't presume to know what your baby is like, but I think in most cases it's not overly difficult to do some basic maintenance during the day to keep things presentable - washing dishes, chucking on a load of washing.
In your situation, my husband would be pulling his weight, since anything less for either of us is unacceptable. Whoever was working long hours would take over the childcare as soon as they got home, as they need to make the most of the time spent with their children. The other would do any housework which couldn't be done during the day. This means both of us would be able to sit back on the couch about the same time, and the weekends would be free-er to relax and enjoy ourselves.