Place beets in a pot with water to cover. Bring to a boil and cook for 30 minutes. Remove skin and puree beets in a blender or food processor.
Preheat the oven to 375 degrees F (190 degrees C). Butter a 9x13-inch baking pan.
Melt butter in a saucepan over low heat. Add unsweetened chocolate and stir until melted. Set aside to cool.
Combine all-purpose flour, whole wheat flour, baking soda, and salt in a small bowl.
Beat sugar and eggs together in a large bowl using an electric mixer until creamy. Add the melted chocolate, beets, and vanilla extract. Beat until combined.
Stir the flour mixture and chocolate chips into the beet mixture just until combined. Pour batter into the prepared pan.
Bake in the preheated oven until a fork inserted into the center comes out clean, about 40 minutes.
