User has a normal looking credit / debit card. Bank account shows local currency, we'll use dollars. User deposits 100$.

Underneath, the users actual account is represented by monero. For simplicities sake, let's put them at parity. So user has 100 xmr in account. Bank has + 100$.

User buys something at a store that costs 5$. On backend a monero transaction occurs between the users monero account and the stores account. The payment processor could manage both of these accounts. Now the stores account has 5 Xmr.

Of course the store sees it as 5$. If the store wants to cash out, bank just transfers xmr to the general bank account and pays out the 5$.

And of course one can see that if the bank was sending 5$ to another bank, for instance to pay for supplies etc, they could just send monero.

One can also see that one could use any amount of xmr to represent the fiat. It's just using it as a ledger.

One could ask, why the hell bother? Because by using monero, the only thing visible is that the there was a transaction. No one knows that the user spent 5$, and no one knows the store got 5$.

Furthermore, it's as secure as we can make it. Once we figure a way to make a transaction signed by a credit card, the only database to hack is the block chain.