There's the money and there's the workload.
If he's working 30 hours pw, and you're studying for 40 and doing some work on top, he should be doing more housework / cooking etc than you are, of course.
You should both get the same amount of downtime - that's the only fair way to go about it.
When you choose to join households, that's what you're doing. I don't understand the theory that because you have more children you should be doing more of the work. If he thought that, he shouldn't have moved in with you. I couldn't sit relaxing watching the person I love run off their feet and getting less rest than me.
In any case, he chose to cut his hours, and refuses overtime. There was no good reason for that other than he wanted to work less. The only good reason for that would have been that he wanted to work less so he could take some pressure off you at home. But he hasn't done that. He works fewer hours than you, and he does less at home.
As pp have said, I can sort of see that as you have 5 children you might have expected your expenses to be higher than his, but again, in a loving relationship, why would you watch your DP struggling and scrimping (and buying treats for your own children) while you squander the 'spare' money you have left? I can't imagine it.
If he feels strongly that's how you should treat your income, he will no doubt think that's the case when you're earning twice as much when you've qualified. He can't have it both ways.