OMG ignore people who think you should be doing all the housework!! Especially the one who has one (1) 1 year old in nursery!!
You have a THREE MONTH old baby and a two year old. It's completely likely you will get no down time, no naps, hardly any food, a significantly broken night, and be very very tired and recovering from birth.
You are at home and can adjust your schedule to get that time - eg a nap on the sofa while you pop a movie on for the kids etc or an online fitness
I can't even. A three month old could be contact napping all the time, and you need to prep food for the two year old and sort out urgent cleaning like nappies and toddler doing a poo on the carpet etc. This poster is bonkers unrealistic.
So! To the husband. There is no way he should be energetic enough to go out with his mates on Saturday nights if he is pulling his weight, at this stage. Maybe in a year.
You need to tell him very firmly the following:-
You are doing far more hours than him. It is deeply unfair and may lead to you leaving him and if you do there will be days when he is responsible for work AND children.
He isn't even "bringing in all the money" you have SMP and a job to go back to.
He thinks he's earning enough to cover all your expenses and the children's care and expenses and all the unpaid work you are doing in the house so he should not have any extra to do. I guarantee he is NOT earning enough to cover FT childcare, plus cooking, laundry, housework and admin for the children. Plus cooking and housework for him, to the extent that he doesn't need to do any (even with no kids a single working man has some housework to do). So his sense that it's fair because he earns the money is wrong. He is not earning enough to cover not thinking about this stuff. His money does not cover his Sunday lie in.
Emotionally, how can he see you struggle? I don't think that's an argument to use with him as he won't care, but for yourself...are you sure this is what you want?