Preheat the oven to 350°F and grease 3 8-inch round cake pans liberally with butter.
In a medium-sized mixing bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.
Cream together the butter, oil, sugar, and vanilla until fluffy and significantly lighter in color. Mix in the eggs, one at a time.
Mix half of the dry ingredients into the butter mixture. Slowly mix in the buttermilk and then the milk. Mix in the key lime juice and zest followed by the remaining dry ingredients.
Divide the batter between the 3 cake pans and bake for 23 minutes or until a toothpick inserted in the center comes out clean.
Remove the cakes from the oven and allow them to cool in their pans for 10 minutes before turning them out onto wire racks to cool completely.
Make the Frosting:
Mix together the cream cheese and butter on medium speed until well combined. On low speed, mix in half of the powdered sugar followed by the key lime juice and zest. Finally, mix in the remaining powdered sugar.
With a long, serrated knife, cut the domes off of the cake layers. Place a cake layer on a serving platter and spread 1 cup of frosting over the top. Add another cake layer to the top and spread another cup of frosting over it. Repeat with the last cake layer and more frosting.
With the remaining frosting, frost the outside of the cake and pipe swirls around the top edge of the cake. Sprinkle the top of the cake with key lime zest and garnish with key lime slices.