How can I change the account billed for an Music family membership?

I recently inputted store credit to my account, and I am worried that my Music family membership will deduct from my iTunes store credit. I am not the family organizer, but the subscription management only shows up in my account, and the receipts show the membership billed to me. Thus, I have come to believe that Apple is charging my account for the membership. Is there a way to change the account that is being charged for the membership? If I cancel auto-renew and then sign up to Music membership from the family organizer's account, will all my music libraries remain intact?