For filling, in a large bowl combine the cream cheese, powdered sugar, and the 3 tablespoons liqueur. Beat with an electric mixer on medium speed until blended and smooth. Stir in 1/2 cup of the whipped dessert topping. Set aside.
For the frosting, in a medium bowl combine the remaining whipped dessert topping, the sour cream, and 2 tablespoons liqueur. Set aside.
Using a serrated knife, cut the angel food cake horizontally into 3 layers. Place 1 layer on a serving platter and the remaining 2 layers on large dinner plates. With a long-tined form or a skewer, poke holes in the tops of all 3 layers.
In a small bowl combine the coffee and 2 tablespoons liqueur; drizzle over all 3 layers.
Spread the bottom layer with half of the filling. Add the middle layer and spread on the remaining filling. Add the top layer. Frost cake with frosting.
Serve immediately, or cover and chill in the refrigerator for up to 4 hours.