Your list is more than reasonable.
I've done both WOHM and SAHM, and am now lucky enough to be working but with a partner at home...I do not kid myself that my job is more tiring than his! Looking after children all day is no picnic. Of course he's tired, but so are you. You are doing a full time job the same as him. (If he had to employ someone to replace you, how much would it cost him? Nanny, chef, cleaner, ironing lady etc)
On top of this, you are unwell, recovering from surgery and sleep deprived. He needs to grow up and support you like a man, not a teenage boy.
If it makes you feel better, my DH and I have been where you are. It took him longer than me to realise just how much work being a parent entailed, and to pull his weight effectively. Two years on he's a SAHD and loving it and I can't fault him.
So perhaps my 'leave him' comment was hasty, but he needs to understand exactly what you need from him. Give him the opportunity to put his side as long as he's calm. With us, my DH felt I was too controlling and didn't trust him with the DCs. I'd criticise what he'd dressed them in or fed them, without meaning to.
If he's worth 'working on' you'll manage it. But I want to repeat, looking after yourself is your main priority first of all. Happy mum=happy family.
Sorry for rambling, I'm off to bed now.