1. Prepare pudding mix according to package directions, using 1 3/4 cups fat-free milk. Set aside.
2. Combine cream cheese, peanut butter, and sugar in a large bowl; beat with a mixer at medium speed until blended and smooth. Gradually add pudding, beating until well blended. Fold in 1 cup whipped topping.
3. Arrange banana in bottom of crust; drizzle with caramel. Spoon peanut butter mixture into prepared crust; cover and freeze 1 hour. Spread remaining whipped topping evenly over pie. Freeze 8 hours or overnight.