Joint account at separate bank each partner contributes what is needed to pay all the bills (including mortgage) plus $100 - $200 monthly. This should cover utilities, cable, groceries, etc.

Partner A "charges" rent to Partner B at FMV or FMV less a "Partner" discount. This may work out where A is paying 65% or mortgage and B is paying 35% more or less.

If partnership continues and A sells the house then of course, the proceeds could go toward the new house. At this point all money becomes "our" money. How to to spend and how much to save is a joint decision.

If partnership ceases then B leaves and joint account is closed. Remaining funds could be split equally or a portion gifted to B based on the percentage of mortgage covered by former "rent" agreement.