Preheat the oven to 350°F. Grease a 9 × 5 × 3-inch loaf pan.
Cream the butter and sugar until light and fluffy. Add the eggs, one at a time, beating well after each addition.
Sift the all-purpose flour, baking soda, and salt together, stir in the whole-wheat flour, and add to the creamed mixture, mixing well.
Fold in the mashed bananas, vanilla, and walnuts.
Pour the mixture into the prepared pan. Bake on the center rack of the oven until a cake tester inserted in the center comes out clean, 50 to 60 minutes. Cool in the pan for 10 minutes, then on a rack.