Add the vanilla pudding mix, banana cream pudding mix, and cold milk to a large bowl. Beat with an electric mixer for 2–3 minutes until thickened.
In a separate bowl, beat the cream cheese, vanilla extract, cinnamon, and sweetened condensed milk until smooth and creamy.
Gently fold the cream cheese mixture into the pudding, then fold in one container of whipped topping until fluffy.
Begin layering the Strawberry Banana Pudding by spreading a small amount of pudding into the bottom of your dish.
Add layers of Chessman cookies, Nilla wafers, banana slices, strawberries, and strawberry glaze.
Repeat the layers until ingredients are used, finishing with pudding on top.
Spread the remaining whipped topping evenly over the final layer. Garnish with extra strawberries, crushed wafers, and glaze if desired.
Cover lightly and refrigerate for at least 30 minutes, preferably overnight, before serving.