Preheat the oven to 425°F. Spray an 8x8-inch baking pan with non-stick cooking spray.
In a small bowl or measuring cup, combine the milk and lemon juice. Set aside for 5 minutes.
In a large bowl, whisk together the mayonnaise, milk mixture, and melted butter.
In a medium bowl, whisk together the cornmeal, flour, baking powder, baking soda, and salt.
Add the cornmeal-flour mixture to the mayonnaise-milk mixture, whisking just until combined. Let the batter rest for 10 minutes, allowing the cornmeal to absorb some of the moisture.
Pour the batter into the prepared pan. Bake for 18 minutes, until a toothpick inserted in the center comes out clean. Cool for about 10 minutes then cut into squares and serve.