Preheat your oven to 350°F (175°C). Grease a 9x5-inch loaf pan or line it with parchment paper.
In a large mixing bowl, cream together the softened butter, granulated sugar, and brown sugar until light and fluffy.
Add the mashed bananas, eggs, and vanilla extract to the butter mixture. Mix until well combined.
In a separate bowl, whisk together the flour, baking soda, and salt. Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Gently fold in the diced strawberries and blueberries, being careful not to overmix.
Pour the batter into the prepared loaf pan and smooth the top with a spatula.
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.