debit something against someone or something
to record a charge for something against someone's account or against a particular category of an account. I will have to debit this against your account. The clerk debited the charge against you.
debit something to someone or something
to make a charge for something to someone or something. To whose account can we debit this charge? Let's debit it to Jane.
debit something with something
to charge something for something. They debited Fred's account with the whole expense. The bank debited my checking account with the cost of the new checks.