PREPARE cake batter and bake as directed on package for 2 (9-inch) round cakes, blending dry pudding mix and coffee into batter before pouring into prepared pans. Cool cakes in pans 10 min. Invert cakes onto wire racks; gently remove pans. Cool cakes completely.
MEANWHILE, melt white and dark chocolates (separately) as directed on packages. Drop spoonfuls of chocolates alternately onto parchment-covered rimmed baking sheet; swirl gently with knife. Freeze 15 min. or until firm.
BEAT cream cheese, milk and vanilla in medium bowl with mixer until blended. Gradually beat in sugar. Gently stir in COOL WHIP.
CUT each cake horizontally in half to form 2 layers. Stack layers on plate, spreading 1 cup COOL WHIP mixture onto each of the first 3 layers to 1 inch of edge. Spread top with remaining COOL WHIP mixture.
BREAK chocolate into 1- to 2-inch pieces; stand in COOL WHIP mixture on top of cake.