What I meant is if I was to pay for the program, would he have to pay to use it on the same computer?
No, you wouldn't have to pay twice for you both to use Minecraft. It uses a login system, then dowloads the files to the hard drive in order to play the game. It can remember the login information so on each visit either of you could play, one at a time, on the same worlds.
Unless...
we prefer to have separate profiles in games.
In which case, you'd probably have to both purchase separately. I believe that would allow you to keep achievements, stats, character skins etc separate from each other (but I'm not 100% sure on that count).