Flatten chicken breasts to 1/4 inch thickness. Coat chicken with flour. In a large skillet, brown chicken in 2 tablespoons butter (both sides). Put into an 11"x7"x2" greased baking dish. In same skillet, saute mushrooms in remaining butter until tender. Add broth, salt, and pepper. Bring to a boil and cook for 5 minutes or until liquid is reduced to 1/2 cup. Spoon over chicken. Bake uncovered at 375° for 15 minutes. Sprinkle with cheeses and green onions. Bake 5 minutes longer or until chicken juices run clear.