I'm guessing you (as a couple) didn't consider him taking a few months' parental leave? Such a missed opportunity.... and shows why it's so important that couples take it up. If he was in your position, do you think the income would magically become joint? Because I do.
The reason the money he is earning at present is joint is because he's taken on earning 100% of the household income (his 50% and your 50%), in exchange for you taking on 100% of the childcare duties during the day (your 50% and his 50%). Some women also take on 100% of the daily chores too (his 50% and your 50%).
If he's now saying that the money he earns isn't 50% yours... well, then he'll need to start doing his 50% childcare. If his job isn't compatible, he'll need to change jobs or go part-time, or do flexi-working, or any of the other solutions other parents use. Yes, it will be inconvenient, and it will impact the family finances, which is why many couples find it efficient to have one person stay at home!.
I agree he probably doesn't want you to go back to work because it will impact on his flexibility, but I think it's important you do. This baby is his as well as yours, and you can't be the only one sacrificing to accommodate it. Has anything really changed in his life since you had the baby?
What will happen when you finish mat leave? Will you be doing all drop-offs / pick-ups?
Start charging him for childcare & housekeeping if he feels like that.
This is the most ridiculous response to threads like this.
As she could only charge him half (since the kids are hers as well) and since he could then respond with charging her for half the Bill's, it's not going to help the op.
I see this argument appear sometimes, and it just hasn't been thought through.
At the moment he says the money all belongs to him. He pays all the bills. And he gets to decide what the left-over money is spent on... because it all belongs to him.
If OP bills for her work, he's forced to pass some of his income to her (in payment for his half of childcare). Then both of them pay the bills. And both of them (potentially) have money left over.
Following the logic through undermines the argument that the man is the only one paying the bills, which is often something that's thrown in the face of SAHMs and used to justify why the man gets special treatment (lie-ins / no chores in the evening / hobby-time etc).
In this specific case, the OP is likely to come out of the argument quite well, since she could state that she doesn't have a mortgage to pay, and therefore much lower bills...