In large mixer bowl, sift together flour, sugar, baking powder, soda, and salt.
Add butter, vegetable shortening, vanilla, and 3/4 cup of the buttermilk; blend at low speed of electric mixer until moistened.
Beat 2 minutes at medium speed.
Add remaining buttermilk and egg whites.
Beat 2 minutes more at medium speed.
Pour into 2 greased and floured 9x1 1/2 inch round layer pans.
Bake at 350° for 25 to 30 minutes.
Cool.
Spread Lime Filling between layers.
Frost sides of top of cake with Fluffy Frosting.
Garnish top with Toasted Coconut.
Lime Filling: In medium saucepan, blend 3/4 cup sugar and 2 tablespoons cornstarch.
Gradually stir in 2/3 cup water.
Add 2 slightly beaten egg yolks and 1/3 cup lime juice; blend.
Cook and stir over medium heat until mixture thickens.
Remove from heat; stir in 1 teaspoon grated lime peel, 2 tablespoons butter, and 1 drop green food coloring.
Cool.