Preheat your oven to 350°F (175°C). Grease a 9x5-inch loaf pan and set aside.
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.
In a large mixing bowl, beat the softened butter and cream cheese together until smooth and creamy.
Gradually add the granulated sugar to the butter and cream cheese mixture, beating until light and fluffy.
Add the eggs one at a time, mixing well after each addition. Then stir in the lemon zest, lemon juice, and vanilla extract.
Gradually add the dry ingredients to the wet ingredients, mixing just until combined. Do not overmix.
Pour the batter into the prepared loaf pan and smooth the top.
Bake for 55-65 minutes, or until a toothpick inserted into the center comes out clean.
Allow the bread to cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.