Divide dough into three portions. Cover and chill two portions. On a floured surface, roll remaining dough into a 9-in. circle, about 1/8 in. thick.
Transfer to an ungreased baking sheet. Bake at 350° for 7-9 minutes or until lightly browned. Cool for 2 minutes; carefully remove to a wire rack to cool. Repeat twice.
In a large bowl, beat cream cheese and confectioners' sugar until smooth. In a large bowl, whisk milk and pudding mix for 2 minutes; beat into cream cheese mixture. Fold in 1 cup whipped topping. Cover and chill for at least 15 minutes.
Place one cookie layer on a serving plate. Top with 3/4 cup pudding mixture and 1/3 cup each blueberries and raspberries. Repeat. Top with remaining cookie layer; spread with 1/2 cup pudding mixture.
Pipe remaining whipped topping and pudding mixture over the top. Garnish with cookies and remaining berries.