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.
In a large bowl, beat the softened butter and cream cheese together until smooth and creamy.
Add the granulated sugar to the butter and cream cheese mixture, and beat until well combined.
Add the eggs one at a time, mixing well after each addition.
Stir in the lemon zest, lemon juice, and vanilla extract until fully incorporated.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Do not overmix.
Pour the batter into the prepared loaf pan and smooth the top with a spatula.
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 before transferring it to a wire rack to cool completely.