Overlapping faces

Whenever I have two coplanar faces overlapping, the overlapping bit is blurry. Is there a way to keep both faces at the same elevation, but somehow assign one of them as the top, so it’s face hides the other where they overlap?

You are getting what is called Z-fighting. It’s an artifact from OpenGL not being able to discern which face is supposed to be in front. As SketchUp is a 3D modeling application, the way you define one zero-thickness face as being in front of another is with distance between them.