In large mixing bowl, combine milk, sweetened condensed milk, pudding mix, and vanilla. Stir until thoroughly combined.
Fold in whipped cream until combined. Don't use a mixer: folding allows the dessert to be creamier.
In 9x13 pan, start with a layer of vanilla wafers, covering the bottom. Then add your mixture until that layer is covered (spread it around with a spatula). Then add a layer of bananas, followed by more of the mixture, then cookies, etc. The precise order doesn't matter so much.
Cover and refrigerate for at least one hour.