Your job on mat leave is to look after the baby. While they are not sleeping at least, the vast majority of other household tasks should be shared.
Is your husband refusing to do his share because you're at home and he feels like this means you should be doing it all? Or does he acknowledge that he should do his share but just cant be arsed?
If the former then I think you need to leave him with the baby more so he realises that it's impossible to do all the housework with a young kid. Suggest sharing paternity leave for the last few months and him doing everything house related since he thinks this is a fair split of activities.
If the latter you need a sit down chat to really hammer home how this will affect your marriage long term. It's not a problem that will get better - apart from the sleep deprivation, in some ways toddlers are harder work and make much more mess than a baby (I had one who's favourite game was to take everything out of all cupboards and empty everything- food packets, bookshelves, boxes of games like cards, it was a full time job trying to keep up with them). When they start nursery and school as well the mental load increases with everything you have to organise and you will no doubt end up doing his share too. You will end up resenting him and that kills a marriage. You will break up over this. Maybe you could suggest couples counselling which at least will show how seriously you are taking it and also maybe they can get through to him how unfair it is.
Other things you can consider -
Becoming a SAHP. He cant expect you to be a housekeeper and work, he can pick one or the other. If he wants you to do his share of housework then he does your share of earning money. I woukdnt recommend this but it could form part of the discussions
Lower your standards. Lots of people on mumsnet complain about housework but then they also do things like Hoover every day and change bedding every few days and towels after every use etc. Nothing bad will happen if you change beds and towels every other week or hoover once a week instead of daily and wear clothes a couple of times before washing, stop ironing anything etc.
Get a cleaner. If he cant do his share then someone else can.
Ask him what the solution is. Because you doing everything isnt it. If he says he will do more, ask for specifics and also ask what will happen if he doesn't because history has shown this to be the case and it's not fair to make you into the role of housework nag or manager