Yes. When you have a joint account, each account holder is responsible for the full amount of the balance. The credit card company can seek to collect the amount due from either account holder.
If you no longer want to be responsible for the joint account, contact your credit card company to learn your options. You may have to close the account to avoid being responsible for future charges. If you close the account, each of the joint account holders will be responsible to repay the entire balance when you close the account.
See Also
Frozen Bank Accounts
