Welcome to the Apple Support Communities!
I understand you have a question about the billing for the Apple Music Family plan. As the organizer, your credit card on file is used to pay for the Apple Music Family plan. You can not use an iTunes gift card for this purpose.
However, your individual family members can purchase iTunes gift cards in retail stores and redeem to their own Apple ID account so that you won't be charged for their purchases. Take a look at the resources below:
Family purchases and payments
Payment methods that you can use in the iTunes Store, App Store, and iBooks Store
Redeem App Store & iTunes Gift Cards, Apple Music Gift Cards, and content codes