Preheat oven to 375 degrees. Boil chicken breasts in water until cooked thru. Place in cold water to cool. Shred chicken. In large bowl, mix shredded chicken with cheeses, soup, beans, green chilis, sour cream, and milk.
Place 1/2 can enchilada sauce into pie dish and dip tortillas, covering both sides. Place 1/2 cup of chicken mixture onto each tortilla, roll, and place in 9x13 casserole dish coated with 1 cup of enchilada sauce. Continue until all chicken mixture is used. You may need to place a double layer of enchiladas in casserole dish.
Bake uncovered for 30 minutes or until cooked thru.
Heat remaining enchilada sauce in small dish and spread over enchiladas when served.