Combine the cheeses; sprinkle half into a greased 13-in. x 9-in. baking dish. In a large skillet, saute the mushrooms, onion and peppers in butter until crisp-tender. Sprinkle over the cheese. Add the potatoes and ham. Sprinkle with remaining cheese. In a large bowl, combine the flour, parsley, salt and pepper. Add the eggs and milk; mix until smooth. Pour over the top.
Bake, uncovered, at 350° for 35-45 minutes or until a knife inserted near the center comes out clean. Let stand for 10 minutes before serving. Yield: 8-12 servings.