Using Touch ID OR password to unlock?

You can use either

 

I think it does both automatically. You can just rest your finger to unlock using Touch ID, or swipe the screen to be asked to enter password. I know you have to set a password anyways, even if you use Touch ID (in case Touch ID fails, and to re-authenticate every so often), so you should be fine.

Alternatively, you can set up 5 fingerprints, so you could have your girlfriend add hers into the mix as well so she could use Touch ID.

However you want to set it up

 

It always can be unlocked using both. I pretty much only use TouchID to unlock, but if you click and swipe the screen, you'll be presented with the passcode unlock. At that point you can enter your passcode, or you can just put your finger on the home button and it will unlock.

As for significant others, if you trust them and they use your phone a lot, you can also register her finger as one of your fingerprints. My phone's 5 slots are taken up with my two thumbs, two index fingers, and my wife's right thumb, so she can just pick up the phone if she needs to use it for a second (which isn't often, since she has a 5).