In my experience you will need to re-model the parts such that there is zero interference. You can't occupy the same area with two meshes.
I would remodel as James proposed. To make things easier, split your pot up into respective parts and create an assembly instead of one part with different solid parts, doing this will allow your separate materials. Without your files to show us how everything is modeled and set up, it is difficult to pin point the exact cause of your mesh issue, but my experience is the same as James'.