Todd, what is the material you used to make this out of, is it just plain plywood? Was there any bowing in either piece, before you glued the two together? When you did the glue-up, did you lay the project flat with weight on top of it to keep it flat? Looking at it, it looks as if the side that has had paint applied to it, is causing the bowing. You may be able to correct it by painting the back of the backer, and by adding a poly finish to the front of the piece. Don't try to use a water base finish, it has to be a poly or lacquer type. Don't apply the finish to the front or back of the item, until you have a way to clamp or hold it flat. And then, only apply the finish to one side, either the front or back, it doesn't matter which is done first. Let the finish dry until it is good and dry, then finish the other side. The main thing, is to keep it clamped flat for this to work.
Len