Preheat oven to 350 degrees F. Melt butter in skillet; add chicken pieces. Cook over medium-high heat until chicken is lightly browned. Add mushrooms, continue cooking until chicken is no longer pink and mushrooms are tender.
Spread 1/2 cup of sauce into greased 13x9-inch baking dish. Arrange single layer of frozen ravioli over sauce, drizzle 3/4 cup of sauce evenly over ravioli. Spread half of chicken mixture then half of bell pepper and top with 1 cup of mozzarella cheese. Repeat with remaining ingredients expect remaining cup of mozzarella cheese and parmesan cheese. Cover tightly with foil.
Bake for 45 minutes. Remove foil, sprinkle with remaining cheeses. Bake uncovered for 15 to 20 minutes or until cheeses are melted. Let stand 15 minutes before serving.