You might be able to find a lender who would let you roll the amount of the judgments into the mortgage loan and pay them off, but I kind of doubt it. Lenders are getting much more strict and getting mortgage loans is a lot harder than it used to be.
In CA, if you are married, both people have to be on the mortgage. I work with a woman who's husband has a bankruptcy on his record. They tried to buy a home with just her name and were told that they cannot do that in CA. So, they actually got divorced so she could get a mortgage loan. Once she signed, they ran to the Justice of the Peace and got remarried.
When my hubby and I applied for our mortgage loan, there were some things on his credit report that actually belonged to his son. They were very small so rather than to try to get it taken off his credit report and put on his son's we just paid them. They weren't judgments though - just collections.
You might be better served to take the money you've saved for a down payment and pay off the judgments and then work on strengthening your credit scores. The higher your scores, the better interest rate you'll get. A good interest rate can save you thousands of dollars over the long run.
As for the judgment that's only half yours, it will stay on your credit report until the entire judgment is paid in full so you may end up having to pay all of it in order to clear your credit. The creditor is not obligated to divide the debt equally between two people. They can and will collect from whomever has the money. Then it's up to you to go after the other person for reimbursement.