Line a 13x9-inch pan with foil and leave 2 inches overhanging on the ends of pan.
In a large bowl, beat vanilla pudding mix and 1-1/2 cups milk with whisk for 2 minutes. Stir in 1 cup whipped topping.
Repeat in a separate bowl with chocolate pudding mix, remaining milk and remaining whipped topping.
Break 1 graham square in half; coarsely crush 7 of the remaining graham squares. Arrange 14 graham squares and 1 graham rectangle on bottom of prepared pan; cover with vanilla pudding, remaining graham pieces and chocolate pudding.
Refrigerate for 4 hours. When ready to serve, use foil handles to lift dessert from pan; top with bananas and crushed grahams.