Touch ID and password at the same time? Is it possible to require both Touch ID and a password in order to unlock an iPhone?
It's not only possible – it's mandatory!

Apple knew that they can't trust their fingerprint sensor to work 100% of the time, so they won't even allow you to enable Touch ID unless you also set a passcode. Once you've set them up, they're both equally capable of unlocking your phone. You can either "slide to unlock" and enter your passcode or just scan your fingerprint - whatever you prefer!

Edit for your clarification: Sorry for the misunderstanding! No, there's no way (Apple-approved; I'm not sure what jailbroken solutions exist) to have both layers of security at once. Either one can unlock your phone, but there's no way to require both. Like I said, Apple wants to always have a workaround for when the admittedly-fallible Touch ID reads a false negative. They'd never allow Touch ID to be an absolutely necessary component of the only way into your phone.