In a large bowl, combine the soups, tomatoes and green chile peppers and milk. Mix well until smooth. Layer a 9x13 inch baking dish with the tortilla chips, then the chicken, and then pour the soup mixture over.
Bake at 375 degrees F (190 degrees C) for 20 minutes. Remove from oven, top with the cheese and bake for 10 more minutes, or until cheese is bubbly.
