How to paint over mold to prevent it from coming back again

Stains will usually come right through a new coat of paint.

Did you prime it first? In my experience I've found that a good oil (or even better, shellac) based primer works best for keeping stains from bleeding through the paint.

Mold needs three (or really four) things to grow: Stagnant air, moisture/humidity, and dim or dark areas with organic 'food'. The solution you're looking for probably involves using a permanent waterproof barrier (either a paint product -- which would be an industrial coating -- or a foundation product) in order to largely remove the humidity from the equation. Those coatings would need to be installed by a professional. As a cheaper and DIY solution, you might also consider 6mil plastic vapor barrier on the back side of the wallboard.