Slice strawberries and toss with a tablespoon of sugar. Let them sit 10 minutes to release juices and sweeten naturally. Slice bananas into ¼-inch rounds right before assembly. Immediately toss banana slices in lemon juice to prevent browning. Don't skip this step or your bananas will look gross within hours. This prevents oxidation in your strawberry banana pudding.
Beat cream cheese until smooth with no lumps. Whisk instant pudding mix with cold milk for 2 minutes until thick. Fold in sweetened condensed milk for extra creaminess. Gently fold in half the Cool Whip until combined. Don't overmix or you'll deflate the whipped topping. Mixture should be thick and fluffy for proper layering.
Start with vanilla wafers covering the bottom of your dish. Add half the pudding mixture and spread evenly. Layer half the lemon-coated bananas over pudding. Add half the macerated strawberries with their juices. Repeat layers: wafers, remaining pudding, bananas, strawberries. Top with remaining Cool Whip and smooth the surface.
Cover tightly with plastic wrap touching the surface. Refrigerate for at least 4 hours, overnight is even better. The wafers need time to soften and layers need to set. Don't try to serve it early or everything slides around. Garnish with fresh strawberry slices just before serving. Should have softened wafers, creamy pudding, and fresh fruit when your strawberry banana pudding is done right.