Cream butter; gradually add sugar, beating with electric mixer until light and fluffy.
Combine dry ingredients. Add flour mixture to creamed mixture alternately with milk, beginning and ending with flour mixture. Stir in vanilla.
Beat egg whites (at room temperature) until stiff peaks form; fold into batter.
Pour batter into 3 greased and floured 9-inch round cake pans. Bake at 375° for 20 minutes or until a wooden pick inserted in center comes out clean. Cool in pans 10 minutes; remove from pans, and let cool completely.
Spread filling between layers of cake; spread top and sides of cake with frosting.