If the host has a co-op partner in her lobby at the point of character creation, then you both create your own, otherwise the host creates both characters and can invite co-op players in whenever they fancy. If you share the creation process with another, that character isn't tied to the specific other player in any way. You as the host are able to continue playing in single player controlling the whole party, inviting other, different players if you wish, whatever. Ultimately it's the host's game. Any co-op partners you invite are just guesting in your save file, controlling all aspects of the second 'main' character but only doing so for the duration of your session.
Edit: importantly, the game supports multiple profiles so you can have separate playthroughs running concurrently.