Beat cream cheese and dry pudding mixes in large bowl with mixer until blended, gradually beat in milk. Gently stir in Cool Whip or homemade whipped cream, reserving 1/2 cup.
Spread a thin layer of cool whip in a 9" x 13" pan just to coat the bottom.
Layer 5 graham crackers across the center of the pan then 2 more; breaking them as needed to fit around the top and bottom edges.
Spread a layer of pudding mixture over grahams and top with a layer of blueberries and sliced strawberries.
Place graham crackers on top of berries, then pudding mixture, then layer of berries again.
Repeat the graham-pudding-berries layers 1 more time (3 times total) and you should reach the top of the pan.
Refrigerate for at least 4 hours or overnight until the graham crackers have softened completely.
When ready to serve, melt white chocolate chips in a bowl as directed on package and drizzle over dessert.