Your partner was able to continue working while you took maternity leave, this has a huge impact on your long term earning capacity. He is being completely unreasonable. The decision to have children should be one which does not impact women unequally, but it does, from the physical burdens of pregnancy,, the enormous impact on lifetime earnings, the mental.and physical load of parenting.
He is saving, investing in his pension and requiring you to contribute to 50% of the household expenses while earning 3 times your salary, demanding that you pay your way. Tell him that you have paid your way, by bringing your children here and taking maternity leave.
You have not benefited from his increase in salary, there is no way that you should be paying back the child benefit, 100% of it should come from his savings. He should be paying into savings and pensions.for you, at a minimum to cover the amount you have lost due to the loss of child benefit but in reality, much much more.
He would not have the life he has now, if you had not sacrificed your lifetime earnings to have his children. If you divorced, you would be entitled to a share in his pensions and a share of the family assets including his savings.
He has benefited from the tax rebate associated with the pension payments.... I am guessing that he has not had to pay back £10k (which would be roughly 5 years of child benefit for 2 children) but he has had to pay £10k less the tax refunds associated with his pension payments... do not agree to pay this before you see the full financial picture, how much he is putting into savings, how much he pays into his pensions and the exact amount he paid to HMRC.
What does he think the future looks like... you carry on earning your own salary, pensions etc, contributing 50/50, living frugally, while he sits on his piles of money? Do you share household and family tasks equally? What happens in retirement, you live on beans and toast and he cruises round the world in.luxury?