This isn't about money. This is bizarre.

My dad and stepmom keep separate checking accounts, but they pool the majority of their money for household expenses. They determine who contributes what depending on their average income at the time. So if they're making similar incomes, they each pay for half the household expenses. Then they can use the rest for disposable stuff. They each have their own kids, and like to be able to buy gifts for each other, etc. My dad is a broker so his income varies a lot from year-to-year - this keeps it pretty fair. I never hear them complain.

DH pays for rent and car (though the car will be paid off in a couple of months). I pay for groceries and gas. We split the rest of the bills.

If you split up the bills, it should be roughly based on income. So he should be paying more of those bills. Sounds like should take over at least your largest bill. When we did this, it worked better to do it by bill rather than percentage of bill.

We have separate bank accounts.
He pays mortage and bills.
I pay for all day to day expenses....I have NO idea how it woks out.
I make less than him, but we really don't care. We consider it OUR money....when one of us gets low - the other writes a check.