Lightly spoon flours into dry measuring cups; level with a knife.
Combine flours, oats, baking soda, cinnamon, and salt, stirring with a whisk.
Place sugar, butter, and molasses in a large bowl; beat with a mixer at medium speed until well blended (about 1 minute).
Add eggs, 1 at a time, beating well after each addition.
Add banana, yogurt, and vanilla; beat until blended.
Add flour mixture; beat at low speed just until moist. Spoon batter into an 8 1/2 x 4 1/2-inch loaf pan coated with cooking spray.
Bake at 350 for 1 hour and 5 minutes or until a wooden pick inserted in center comes out clean. Cool 10 minutes in pan on a wire rack; remove from pan. Cool completely on wire rack.