In a separate bowl, sift together the all purpose flour, whole wheat pastry flour, baking powder, baking soda, and salt. Beating well on low speed after each addition add ingredients to the butter-sugar mixture in the following order: 1/3 of the dry ingredients; 1/2 of the buttermilk; the next 1/3 of the dry ingredients; the final 1/2 of the buttermilk; then the remaining dry ingredients. With a rubber spatula, fold in the 6 ounces flaked coconut.
In a large mixing bowl, beat together the sugar, butter, and coconut oil until well blended. Add the eggs, one at a time, beating well after each addition. Beat in the vanilla and almond extracts. The mixture may look a bit curdled, but do not be concerned.
Place rack in upper and lower thirds of oven and preheat oven to 325°. Grease three 9-inch round cake pans with cooking spray, line with parchment paper, the grease again. Set aside.