Preheat oven to 350°F. Generously coat a 9x13 inch pan with nonstick spray.
In a large bowl, mash the bananas.
Whisk in the eggs, granulated sugar, brown sugar, oil, and vanilla.
In a separate medium bowl, combine the all-purpose flour, whole wheat flour, baking powder, baking soda, and salt.
Add half of the dry ingredients to the banana mixture and fold in by hand, just until combined.
Gently stir in buttermilk. Fold in remaining dry ingredients, just until blended, being careful not to over mix.
Pour into the prepared cake pan and smooth the top.
Bake 30 to 35 minutes, until the top of the cake springs back lightly when touched and a toothpick inserted in the center comes out clean. Let cool completely (once the cake nears room temperature, you can pop it into the fridge to speed things along).
While cake cools, prepare the frosting: In a large bowl or the bowl of a stand mixer with a paddle attachment, beat together the cream cheese and butter until smooth and creamy, about 2 minutes. Add the vanilla and almond extracts and then reduce the speed to low. Gradually add the powdered sugar, 1/4 cup at a time, beating just until combined.
Once the cake has cooled completely, spread the frosting over the top. Refrigerate for 20 minutes to allow the frosting to set. Slice and serve.
Notes
TO STORE: Cover the cake and store it in the refrigerator for up to 4 days.
TO FREEZE: Cover the cake layers tightly in plastic wrap, and place in an airtight, freezer-safe storage container in the freezer for up to 3 months. Let thaw overnight in the refrigerator before serving. If you plan to freeze the cake, wait to frost it until after you've thawed it.