Lightly grease 9×13-inch baking dish. Line bottom of dish with half the bread cubes. Sprinkle with ham, Cheddar and Swiss cheeses; top with remaining bread.
In bowl, beat together eggs, milk and onion powder. Pour evenly over bread. Cover; refrigerate overnight.
Preheat oven to 375°. In small bowl, blend crushed cornflakes and melted butter. Spread evenly over casserole.
Bake 40 minutes in preheated oven, or until bubbly and golden brown. Let stand 5 minutes before serving.