I'm sorry to hear your husband is being so difficult.
I am in a similar situation with regard to my DH suffering from back pain. A little background; we have been together 3 years and have a 4 month old DS. He sustained a back injury through work about 2 years ago which resulted in him needing spinal surgery. This injury was caused by his job, which is very hard physical labour (lifting heavy items constantly). He works night shifts between 11pm-7am. I am currently on maternity leave.
My DH does try to help out and is brilliant with our son, in fact as I type this my DH has just got back from work and taken DS downstairs to do the morning routine while I have a lay in. However, he really doesn't do much at all chores-wise since I've been on maternity.
He will do chores if I nag but that always leads to a bit of bickering and frustration, and lots of excuses for why he hasnt done said chore (I didn't sleep well, I feel ill, I was going to do it but you got there first..) which leaves me feeling a bit guilt tripped for asking. He also will complain about back pain while doing said chore (which I do sometimes think he might be over dramatising a little bit. Or maybe I'm just being insensitive). The time spent nagging and bickering I could have just got it done myself while he watches DS. So that has sort of become the norm now and he will watch youtube/play playstation while watching DS and I'll do chores when he's up.
The only thing I REALLY wish he'd do is clean up after himself. First job of the day for me (after feeding DS etc) is clean up empty packets and plates/mugs/bowls from the coffee table and the kitchen side. If I mention anything about them he always says "I was just about to do that" but if I leave them they're there the next day.. grr.
I'm not a picture of health myself, since giving birth I've had a problem with my hips which causes me pain and some limited mobility but I never let it stop me doing anything. Just pop sone painkillers and get on with it (not saying that is what DH should do, I know his back pain is much more severe than my hips).
Your DH would frustrate me no end. I don't agree that him earning more means he sould have more leverage on financial decisions (I earn 2x my DHs salary and don't think that way at all). Do you think he would be open to discussions about all this or would he get defensive/angry? 