Preheat oven to 350 degrees. Spray a 9x13 dish with nonstick spray.
Whisk together milk, half and half, eggs, egg whites, vanilla, cinnamon, and nutmeg in large bowl until blended. Stir in bread and banana; let soak 15 minutes, stirring occasionally.
Spoon the bread mixture into the baking dish. Bake until knife inserted in center comes out clean and the top is lightly browned, about 1 hour.
Sprinkle with powdered sugar. Serve at once.
