Immediately contact the fraud department at your credit card company and tell them you are the victim of identity theft. They may make you fill out a document attesting to the fact that you did not authorize that credit card to be issued.
They will ask if you know who applied for the cards and demand that you fill out a police report regarding this identity theft. If you don't want to have your wife arrested for this, then call the credit card companies and have the cards canceled, converting the balance into a loan and preventing future charges.