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If you pull your 3 reports directly from the CRAs, you'll see a field within the TL that says something like "Responsibility" or something like that. In fact, if you already have your FICO reports, there is a field that says "Account holder" that indicates whether it is an individual account, a joint account, or an AU.
Changing the responsibility might be a challenge. Most CC issuers won't let you change the status after the card is opened. The only way to stop the BK from reporting on that TL (Assuming they included it) would be to PIF and close it before the BK. It would hurt if the CC reported a BK. Worth calling to try though. If you did manage to get yourself off, it won't have any impact on the account or your folk's BK.