Tip: Frost the layers very lightly to preserve the checkerboard effect. Adding gel food coloring will deepen the red hue.
Preheat oven to 325 F.
Lightly coat the cake pans with cooking spray and dust with flour. Set aside. In a medium saucepan over moderate heat, combine frozen raspberries and raspberry syrup. Bring to a simmer, reduce heat to low and continue cooking until liquid reduces by two-thirds.
Remove from heat and strain, pressing on the raspberries to release all the juices. There should be approximately 1 cup. Dispose of the raspberry pulp or reserve for another use. Add the food coloring, if using.
If there is more than 1 cup of juice, put in a small saucepan over medium heat and reduce to 1 cup; cool to room temperature. If there is less than 1 cup, add enough water to equal 1 cup.
In a medium bowl, sift together cake flour, baking powder and salt; set aside.
In the bowl of a stand mixer fitted with the paddle attachment, cream the butter and sugar until light and fluffy. Add the eggs one at a time, beating well after each addition. Beat in the vanilla extract.
Divide the batter in half. To one half of the batter, beat in the 2 cups of the flour mixture alternately with the milk to the batter, beating after each addition until smooth. To the remaining batter, beat in the remaining flour mixture alternately with the raspberry syrup to the batter until smooth.
Place checkerboard divider into one prepared pan. Then spoon in the two batters (red and plain) as described in "How to use your Checkerboard Cake Set."
Place all 3 pans in oven at same time. Rotate pans halfway through baking. Bake approximately 20 to 25 minutes, or until a toothpick inserted in the center comes out clean. Let the cakes rest in the pans, set on a rack, for 10 minutes. Place a cooling rack on top of each cake, invert the cake and remove the pan. Cool completely.
Using no more than 1/4 cup of jam, frost a very thin layer on top of one of the white cakes and on the raspberry cake.
In the bowl of a stand mixer fitted with the paddle attachment, cream the butter and cream cheese on high speed until light and fluffy, approximately 5 minutes. Beat in the almond extract. Reduce the speed to low and carefully drizzle the chocolate into the cream cheese. Increase the speed to high and beat until light and fluffy, about 2 minutes. Add powdered sugar and beat until well incorporated.
Spread a thin layer of frosting on the jam-covered white cake. Place the raspberry cake on top of this cake and spread a thin layer of frosting on top. Place the last white cake on top. Frost the sides and top of the checkerboard cake. Refrigerate until ready to serve.