Heat oven to 350. Spray 9 x 5 loaf pan with nonstick spray,
In a small bowl stir together eggs, milk, applesauce, oil, set aside. In another small bowl stir together flours, soda, and salt, set aside.
In a large bowl beat together sugar, mashed bananas, and vanilla. Alternately add egg mixture and flour mixture, beating at low speed and scraping bowl often just until ingredients are mixed.
Pour into prepared pan. Bake 60 minutes or until toothpick comes out clean. Cool completely before slicing.