In a large skillet, saute frozen green beans in butter until tender. Stir in broth and milk. Stir in the flour, salt, pepper and nutmeg until blended. Bring to a boil; cook and stir until thickened. Stir in Parmesan cheese and broccoli; heat through.
Spread 1/2 cup broccoli mixture in a greased 13-in. x 9-in. baking dish. Place a single layer of noodles, broccoli mixture, 1 cup ham and 1 cup Monterey Jack cheese. Top with another layer of noodles, broccoli mixture, all of the chicken, 1 cup of ham and 1/2 cup Monterey Jack cheese.
Cover and bake at 350° for 45 minutes or until bubbly. Sprinkle with remaining Monterey Jack cheese. Bake until cheese is melted. Let stand for 15 minutes before cutting.