Beat butter at medium speed with an electric mixer until creamy. Add granulated sugar and brown sugar; beat until light and fluffy. Add eggs, 1 at a time, beating until blended after each addition. Beat in bananas at low speed. Increase speed to medium, and gradually add flour mixture to butter mixture alternately with buttermilk, beginning and ending with flour mixture. Pour batter into 2 greased and floured 9-inch round cake pans.
Bake at 350° for 30 minutes or until a wooden pick inserted in center comes out clean.
Cool in pans on wire racks 10 minutes. Remove from pans, and cool completely on wire racks.
Spread Coconut-Cream Cheese Frosting between layers and on top and sides of cake.