Cook peas and beans separately according to package directions; drain well. Layer peas, beans, mushrooms, pepper, and cheese in a 12- x 8- x 2-inch baking dish. Repeat layers, reserving 1/2 cup cheese.
Combine mayonnaise and whipped cream; spread evenly over top of vegetable layers. Sprinkle with reserved cheese. Bake at 350° for 20 minutes or until browned and puffed.