Preheat the oven to 350 degrees F (175 degrees C). Grease a 9x5-inch loaf pan.

Beat white sugar and butter together in a large bowl with an electric mixer until light and fluffy. Add brown sugar and hot chocolate mix; stir well.

Place bananas, peach, eggs, milk, and vanilla in a blender; blend until smooth. Stir into butter mixture until well incorporated.

Mix flour, walnuts, baking soda, and salt in a separate bowl until evenly combined; stir into banana-butter mixture until just moistened. Pour batter into the prepared loaf pan.

Bake in the preheated oven until a toothpick inserted into the center of loaf comes out clean, 50 to 60 minutes. Cool in the pan for 5 minutes, then remove bread to a wire rack to cool completely.