Lightly grease a 9x13 inch baking dish. Line the bottom of the dish with half the bread cubes. Sprinkle with ham, Cheddar cheese, and Swiss cheese, and top with remaining bread. In a bowl, beat together the eggs, milk, and onion powder. Pour evenly over bread. Cover, and refrigerate overnight.
Preheat oven to 375 degrees F (190 degrees C). In a small bowl, blend the crushed cornflakes and melted butter. Spread evenly over the casserole.
Bake 40 minutes in the preheated oven, or until bubbly and golden brown. Let stand 5 minutes before serving.