Preheat oven to 375°F (190°C) and lightly grease a 9x13 inch baking dish.
In a large mixing bowl, combine the shredded chicken, diced green chiles, black beans, and corn.
Spread 1/2 cup of enchilada sauce over the bottom of the prepared baking dish.
Arrange half of the tortilla strips over the sauce to create an even layer.
Top the tortillas with half of the chicken mixture, 1/2 cup of enchilada sauce, and 1 cup of the blended cheeses.
Repeat with a second layer using the remaining tortilla strips, the rest of the chicken mixture, and 1/2 cup of enchilada sauce.
Pour the remaining enchilada sauce over the top and sprinkle with the remaining 2 cups of cheese.
Bake for 25 to 30 minutes until the cheese is melted, golden brown, and the sauce is bubbling.
Let the casserole rest for 10 minutes before serving. Garnish with sour cream and chopped cilantro.