BEAT cream cheese in medium bowl until creamy. Gradually add sugar, mixing until well blended. Stir in milk. Remove 1/4 cup of the cream cheese mixture; place in small bowl. Stir in flavored instant coffee mix. Drizzle 1 Tbsp. of the coffee-flavored cream cheese mixture onto bottom of crust. Set remaining flavored cream cheese mixture aside.
STIR whipped topping gently into remaining plain cream cheese mixture, stirring just until marbleized. Spoon into crust. Drizzle with remaining coffee-flavored cream cheese mixture. Swirl knife gently through mixtures several times for marble effect.
REFRIGERATE 2 hours or until set. Store leftover pie in refrigerator.