PREHEAT oven to 400°F. Spray 13x9-inch baking pan with cooking spray. Place half each of the eggplant and mushrooms in prepared pan; top with layers of one-third each of both of the cheeses. Repeat all layers.
TOP evenly with spaghetti sauce; cover with foil.
BAKE 35 min. Remove foil. Sprinkle casserole with remaining cheeses. Bake, uncovered, an additional 5 min. or until mozzarella cheese is melted.