His house, eh? Because he's doing all the earning cash outside the home bit?
So by that reckoning, they're not his kids. Because that's the 'bit' he's not doing. They're all yours - and next time he has an opinion on their upbringing/schools/bedtime etc., you can tell him it's none of his business... oh and he has to ask you first if he wants to go to their graduations/weddings/etc....
Yes, thought not!
Sigh. This is a really SIMPLE one.
You are a family. A family where the tasks are split with different people doing different tasks. One of these is working outside the home doing a task for other people, you get given bits of paper for doing it which you exchange for things you need like loo roll, cars, and baked beans. That is his task. There is another set of tasks mainly concentrated inside the home, which focus on childcare. If there isn't a person inside the family set onto this task, it is outsourced, and costs lots of the pieces of paper, and you buy far fewer cars/beans/loo roll, or indeed HOUSES!!!
It does not matter who does what task, because they all need to be done in order for the family to function. One task isn't worth more than another, because they all need to be taken care of in order for things to be as they are.
The pieces of paper and the things that are bought with them belong equally to everyone.
How can it be 'his' money? If you weren't there, he wouldn't be able to go out and earn it - all his cash would be going on a nanny. Or, he'd be able to have lots of cash, but no children and nice home and family.
You need to go on the deeds. You have made this family possible just as much as he has, and his career track is defined just as much by the fact that you stay home and raise his children as by what degree/qualifications he has or what jobs he has done. If you weren't there or were working full time, his life would be RADICALLY different. Your home is yours as much as his.
If he disagrees, ask him how he would feel if you decided one day to leave, and take 'your' children, and tell him he had no rights to them, at all, because you did the stay at home bringing them up thing, and his contribution was thus nothing. He'd be enraged. But that is what he is effectively saying to you in terms of the 'working out of the home' side of things.