This is why I will never get myself in this position (relying on a male partner's income).
At heart, some men simply do not value childcare/hands on parenting, or the skill of running a household. Which involves cleaning/laundry/food shopping/cooking but also the 'life admin' of basic organisation - birthdays, school events, timetables etc.
They should value it - but they don't. Sometimes they will SAY that they value it - but their behaviour says otherwise. This is especially true of men that have never done any of that stuff for a significant length of time. Looking after kids on a Saturday is often cherry picking the fun bit of parenting. Doing it for 6 months as the main carer, coping with illness, tiredness, rainy days and having to do other things at the same time is the real slog. A lot of men who never have to do family shopping/budgeting/cooking don't actually know how much things cost, either. So you get the nasty scenario where a mother makes an effort to plan and shop carefully, to be confronted by a man resentful that she is asking him for what HE thinks is a large amount of money, and for which is likely to blame her for.
Other posters are correct that is is your contribution that allows him to work without having to pay for childcare/cleaner etc. 'Billing' him is a nice idea, but unlikely to work, in terms of making him see sense and realise that while he is thinking of you purely as a 'dependent', he is actually depending on you for the continuing operation of his life as it is.
I hope future generations have an easier and more equal time of it. But until men step more into the domestic sphere and experience the reality of it, it's always going to be a difficult area.
(btw, if my male partner was to take more of a step back, and take over more childcare/domestic work than he currently does, I would pay him an agreed monthly salary - not an 'allowance', I loathe that word - for the actual WORK that would involve - but all COSTS of shared living like food etc would be seen as exactly that. SHARED costs, not costs just incurred by him as the main carer)