This is a lovely form. Ideally, Stripe would offer something like this as a way to quickly generate a nice cc entry form with the intention that site owners would put the generated code directly on their site, or that stripe would host the service themselves. After all, you're already trusting them to run the service, might as well trust them to run the form too. Not that it's terribly hard to build a stripe-compatib…
That would defeat the protection which the Same Origin policy gives you (since the iframe would have the same origin as the rest of your site).
or that stripe would host the service themselves
Yes, that would be much better.