Preheat your oven to 350°F (175°C). Grease a 9x5-inch loaf pan with cooking spray or butter.
In a large mixing bowl, combine the mashed bananas, granulated sugar, brown sugar, melted butter, eggs, and 1 teaspoon of vanilla extract. Mix until well combined.
In a separate bowl, whisk together the baking soda, salt, and flour. Gradually add the dry ingredients to the banana mixture, stirring until just combined. Do not overmix.
In another bowl, beat the softened cream cheese, powdered sugar, lemon juice, and 1/2 teaspoon of vanilla extract until smooth and creamy.
Pour half of the banana bread batter into the prepared loaf pan. Spread the cream cheese mixture evenly over the batter, then top with the remaining banana bread batter.
Use a knife to gently swirl the cream cheese filling into the batter for a marbled effect.
Bake in the preheated oven for 55-65 minutes, or until a toothpick inserted into the center comes out clean.
Allow the bread to cool in the pan for about 10 minutes before transferring it to a wire rack to cool completely.