Beat butter and shortening at medium speed with an electric mixer until creamy. Gradually add sugar, beating well. Beat in egg yolks, 1 at a time.
Combine flour and baking soda; add to butter mixture alternately with buttermilk, beginning and ending with flour mixture. Beat at low speed until blended after each addition. Stir in flavorings, coconut, and chopped almonds.
Beat egg whites at high speed with electric mixer until stiff peaks form; fold into batter. Pour into 3 greased and floured 9-inch round cakepans.
Bake at 350° for 20 to 22 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 on wire racks.
Spread Cream Cheese Frosting between layers and on top and sides of cake. Sprinkle with 1/2 cup slivered almonds, if desired.