In the mixing bowl of a stand mixer, blend the butter and vegetable shortening together until smooth and creamy.
Add the powdered sugar a little at a time, and add the heavy cream between additions, also, a little at a time, until all the powdered sugar and cream have been blended into the frosting, and the frosting is smooth and fluffy. Set aside.
Starting with the Chocolate cake, trim off the top of the cake, so that it's even with the pan, and then turn the cake out onto a cake plate or cake stand. Add a generous amount of the buttercream frosting to the top of the cake.
Next, trim off the top of the pumpkin cake, and place that layer on top of the frosting on the chocolate layer. Frost the pumpkin layer with a good amount of frosting. Next, trim off the top of the Vanilla cake, and place it on top of the frosting on the pumpkin layer. Frost the Vanilla layer, and down the sides of the cake, covering the cake in the frosting. Place the cake in the refrigerator.