The black one should have a soft surface to it and always goes against the pad. The stainless one keep the pistons from digging into the black one, so it always goes against the piston. Yes, your right they attach to the pad back and insulate it from the piston. The idea here is to dampen and vibration set up in the brake pad so you don't hear it as a squeal. The anti squeal grease goes on each shim sparingly. You can see they don't give you very much.
Interestingly enough all disc brakes squeal, it is the engineers job to make the squeal happen in a range that you can't hear.
But maybe your dog can.

Mike