Lightly grease 9x13-inch glass baking dish. Beat first 5 ingredients in medium bowl to blend. Arrange chilies from 1 can in prepared dish, covering bottom completely. Sprinkle with 1/3 of each cheese. Repeat layering twice. Pour egg mixture over cheese. Let stand 30 minutes. (Can be prepared 1 day ahead. Cover and refrigerate.)
Preheat oven to 350°F. Bake until casserole is slightly puffed in center and golden brown on edges, about 45 minutes. Cool 20 minutes and serve.
Recipe says 8 servings, but we got 12 out of each 9” x 13” pan. Also we used a lot less cheese than the recipe calls for.