Unfortunately, he cannot use the debit card or credit card to post cash bail at the jail. However, he may be able to get a bail agency to bail him out and then put the premium on his credit card or debit card. If the debit and credit cards are in property, and not booked as evidence, they will be released when he is released from custody.
It would be up to the bail agency to agree to post the bond and then allow him to pay the premium after he is released. I recommend that you call some bail agents to see if they would be willing to handle the posting of bond in this manner.
If he has an attorney, not only may the attorney be able to direct him to a reputable bail bonds, but some agencies are able to charge 8%, rather than the customary 10%, if he is represented by counsel.
Mr. Kent's answer notwithstanding, CC 3531 "the law never requires impossibilities." If it is impossible for you to post bail using your credit card the law cannot require that you do so. An alternative is to use the phone bank inside the jail where you will see that present and former inmates have written down the numbers of the best bail bondsmen. One of them will surely right your wrongs.