Heat oven to 400°F. Spray 13x9-inch (3-quart) baking dish with cooking spray.
In 10-inch nonstick skillet, mix uncooked rice and sauce mix (from Hamburger Helper box), 1 cup of the milk and the hot water. Heat to boiling; reduce heat. Cover; simmer about 15 minutes, stirring occasionally, until rice is tender and most of liquid is absorbed. Remove from heat.
In medium bowl, mix chicken, chiles, black beans and 1 cup of the cheese. In small bowl, mix topping mix (from Hamburger Helper box) and remaining 3 tablespoons milk; cover and refrigerate.
Layer 3 tortillas in baking dish, overlapping as necessary and placing slightly up sides of dish (cut third tortilla in half). Top with about half the chicken mixture, half the rice and half the enchilada sauce. Layer with 3 more tortillas and remaining chicken mixture and rice. Place remaining 2 tortillas over chicken mixture, overlapping slightly (do not place up sides of dish.) Pour remaining enchilada sauce over top. Sprinkle with remaining 1 cup cheese.
Bake uncovered 15 to 20 minutes or until cheese is melted and casserole is bubbling around edges. Drizzle with topping mixture. Serve with remaining ingredients.