I don't think there would be a problem with doing that (using any checking account.) **** The bank won't care whose account they are making a payment on - just that they have the correct payment information (who its going to, address, phone number, and account number) as well as enough funds from the account to make the payment.
Set up the bill (Cap 1) under bill pay on the joint account. Tell your bank to send a payment. The first payment to any creditor usually (not always) may take up to a week or so. The payments after that usually clear very quickly.
My personal preferance is always to push through the payments and NOT allow any creditor to auto debit from my bank accounts.
Shouldn't be a problem for anyone I can think of. I pay mine and my wife's cards from the same bank account. The bank is getting their money; don't know that they receive any account info other than the account number and bank it came out of
I would like to point out something else. Both of you should be on the same page. Both of you should use the card responsibly. No one should suffer due to other person's reckless financial behavior. It can lead to fights later on.