Preheat oven to 350 degrees F (175 degrees C). Lightly grease a 9x5 inch loaf pan.
In a large bowl, cream the butter. Beat in egg, molasses and banana. Mix in whole wheat flour, all-purpose flour, baking soda, salt, nutmeg and walnuts; stir until well blended. Pour batter into prepared pan.
Bake in preheated oven for 55 to 65 minutes, or until a toothpick inserted into center of the loaf comes out clean.