In a large bowl with an electric mixer on medium, beat the cream cheese until smooth and fluffy.
Add sweetened condensed milk, pudding mix, milk and vanilla extract. Mix until well combined. Fold in half of the whipped topping.
To assemble: Layer 13 vanilla wafers on bottom of 9- by 13-inch baking dish; layer with ⅓ of the bananas. Cover with ⅓ of the pudding mixture. Repeat twice. Top with remaining whipped topping.