Normally, the pat answer to this dillema would be that you're out of luck. Banks have what is called a "right of offset", which allows them to deduct any delinquent payments you owe them from a deposit account.
You're case is a bit different in that they are taking money owed for a credit card or revolving line of credit. According to the Comptroller of the Currency, National banks can not exercise their right of offset when the debt is a consumer credit account. As long as this is not a business credit card, it would seem that the bank has overstepped its bounds.
You should check out the Comptroller of the Currency's website here :
http://www.helpwithmybank.gov/faqs/banking_offset.html
And you should follow up with both the C of C and your bank. It seems they may be breaking the law by taking funds from your deposit account to satisfy a credit card debt.
Since banks can deduct money from accounts to satisfy other debts, it would be wise in the future not to have a deposit account at a bank where you have delinquent accounts.