Cook sausage and ground beef in a large skillet over medium-high heat, stirring until meat crumbles and is no longer pink. Drain. Stir in beans and next 5 ingredients; cook until thoroughly heated.
Stir together soups and enchilada sauce in a saucepan; cook until thoroughly heated.
Spoon one-third of sauce onto bottom of a lightly greased 13- x 9-inch baking dish; top with 3 tortillas. Spoon half of beef mixture and one-third of sauce over tortillas; sprinkle with half of Cheddar cheese. Top with 3 tortillas; repeat layers ending with tortillas. Sprinkle with Monterey Jack cheese and next 3 ingredients.
Bake at 350° for 30 minutes. Top with avocado.