Place half the bread cubes in a greased 9×13 baking dish. Sprinkle with half of the following: sauteed onions and peppers, ham, and cheese. Repeat layers.
Remove the dish from the refrigerator 30 minutes before baking. Preheat oven to 350°. Bake, uncovered, until a knife inserted in the center comes out clean, 30-35 minutes.