Spread half the bread cubes level in a lightly oiled 9- by 13-inch baking dish. Top evenly with prosciutto, peppers, green onions, and parmesan cheese. Spread remaining bread cubes level on top, followed by tomatoes, olives, and mozzarella.
In a bowl, whisk eggs, milk, Italian seasoning, salt, and pepper to blend. Pour over layered ingredients. Cover and chill at least 1 hour or up to one day.
Bake in a 325° regular or convection oven until center of strata is set and top is lightly browned, 40 to 50 minutes. Sprinkle evenly with parsley and capers. Let stand 10 minutes, then cut into squares. Serve warm or at room temperature.