In a large mixing bowl, combine softened butter and sugar, and beat with a mixer at medium speed, about 3 minutes or until well combined. Add the egg and applesauce, and beat another 2 minutes. Fold in the bananas.
3
Lightly spoon the all-purpose flour and whole wheat flour into dry measuring cups, and level with a knife. Combine the two flours, baking soda, and salt in a separate large bowl.
4
Add the flour mixture to the banana mixture, 1/2 cup at a time, mixing after each addition until moistened.
5
Coat one loaf pan with cooking spray. Pour the batter into the loaf pan. Tent the pan with aluminum foil.
6
Bake at 350° for 50 minutes to 1 hour, or until a wooden pick inserted in center of the bread comes out clean.
7
Allow the bread to cool in the pan for 5 minutes. Remove the bread and cool completely on a wire rack.