Add milk to dry pudding mix in medium bowl. Beat with wire whisk 2 minutes or until well blended. Stir in 1 cup whipped topping.
Cut cake horizontally into three layers; brush with juice. Place bottom layer on serving plate; top with 3/4 cup mixed berries, half of pudding mixture and middle cake layer. Repeat layers of mixed berries and pudding mixture; cover with top cake layer. Top with 1/2 cup whipped topping and remaining berries; cover loosely with foil.
Refrigerate at least 4 hours or overnight. Store any leftovers in refrigerator.