What material would you suggest to cover fibergl insulation on the inside of a newly built shed?

My carpenter is building me an outside insulated shed for my newly installed oil tank. I was surprised today when he didn't use any covering material on the INSIDE of the fibergl insulation pieces. I don't want to use plastic because of mold/mildew issues, and because it's an outside shed, he didn't think paper was a good idea. Does anyone have any other ideas?