Really? I'm in London, and last Wednesday I happened to see a bank called "The Islamic Bank of Britain" (which, frankly, frightens the living daylights out of me) and it advertises its "profit rates" in the window.
Why does this scare you? Such Muslim banks do not charge interest on loans, essentially they buy an item and then allow an individual to buy the item (usually property) from them in instalments. This is different from other banks in that it is they who own the investment, and therefore they who fail if it fails. Other banks, because they are lending money, allow for speculation and are essentially making money purely because they themselves have it.
I personally find this still quite shady, and while it may be halal (permissible) I don't see it as being tayyib (beneficial).
Though again I ask why it frightens you? The Islamic system of banking, had it had been in place in countries like America, would have stopped the widespread artificial of housing prices beyond any reasonable value, and therefore stopped the last economic collapse.
One could also argue that without the interest made permissible in Britain and Holland, colonialism and the huge amount of exploitation and suffering that came with it, could never have occurred. But I digress.
In any event, the Bible prohibits the charging of interest, specifically between friends and family (including fellow Christians).The Bible doesn't necessarily prohibit earning interest so much as it condemns greed. Earning interest and greed aren't synonymous - it all depends on what you do with the interest you've earned.
So as long as it is charging people you don't no, or infidels, it is permissible? Why is your understanding different to the above? Did the early church practice money lending?
In terms of secular authorities, banking in its current form stemmed from Christian countries, before secularism was invented. I always wonder what exactly in this world is not God's and therefore should not be rendered unto Him. Caesar, in reality, owns nothing. All is God's, surely?