Joint account where all household income goes and all household outgoings go out.
No personal accounts in use.
Monthly "meetings" to do a zero budget with categories and percentages of income, forecasting every single outgoing and allocating every penny of income. We do this together.
We have read and followed Dave Ramsey method for over a decade. The book was Total Money Makeover.
I personally don't think it's right to have separate accounts, for a husband to pay his wife to care for his child, for a wife to have to ask for help or for a husband to watch his wife suffer financially.
If your close enough to love each other, live together and have a child together. There is no longer his/hers, it's the family pot.
I think saying it's old fashioned to getting married is naive. You've had his child and sounds like your now in a vulnerable financial position as there's a power imbalance. You have no financial protection that a marriage offers. It's not a laughing matter?
Even for the financial protection you could have went to registry office.
I think the fact your asking now baby is here maybe points out a gap in your financial literacy that you're seeking to start filling now by asking here. But managing money as a family needs knowledge, work and a team commitment mentality. I do think that should have been hashed out pre-baby.
If someone isn't willing for there to be a family pot, for me that's a red flag and concerning you also have no marriage protection either.
If you were my daughter I'd feel very, very concerned. Sending you best wishes x