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 350F. Bake until casserole is slightly puffed in center and golden brown on edges, about 45 minutes. Cool 20 minutes and serve. Serves 8.