This article is from the Credit cards and Consumer Credit FAQ, by firstname.lastname@example.org (Steve Adams) with numerous contributions by others.
Sorry. If an account is in two names, both are responsible for
paying the bills on time. Unless the report is actually in error,
there's not much you can do as a matter of legal right.
However, you may be able to persuade lenders to give you credit.
Can you show that your record was clean before your marriage, that
it was your spouse who ran up the debts, and that you've arranged
with your creditors to pay them off over time? It's probably best
to visit credit managers in person, and dress like a solid citizen.
If all else fails, you should still be able to get a secured credit
card; see section 3, "Lists of good cards," in part 2 of this list.
By establishing a good record with the secured card, you may
gradually get other lenders to believe in you again.