Can Comp Layers Have Material Shininess?

I have an animation with 3D objects and layers. One of the layers is a comp with an animation in it. I have the comp as a flat, 3D layer and I'd like it to have reflections like a screen. I can add a shape and give it material properties, but the comp does not seem to be affected by changing any material options. Is there a way to give my comp a reflection as it passes by the camera?