Grease three 9x13-inch cake pans with butter and preheat oven to 325°F. Add parchment paper to pans after greasing.
In a stand mixer with a paddle attachment, mix the sugar, almond paste and 1 stick of butter until smooth. Add remaining butter and continue to mix until smooth.
Add egg yolks, milk and almond extract.
Add the flour and mix on low until combined.
In another bowl, whip the egg whites until peaks form. Fold the whipped egg whites into the flour and separate mixture into three bowls. (Add red food coloring to one bowl, green food coloring to one bowl and keep one bowl undyed).
Spread the mixtures into separate pans and bake for 15 minutes.
Let cool, then spread fig jam to cover the top of the green cake and place the undyed layer on top, covering the jam in the middle. Repeat, spreading the remaining fig jam on top of the undyed layer and placing the red layer on top. Refrigerate for 2 hours.
Melt 1 cup of semisweet chocolate chips and add to the top of the cake. Refrigerate for 2 more hours and turn the cake upside down.
Melt another cup of chocolate chips and add to the other side of the cake before refrigerating again for 2 hours. Cut into squares and enjoy!