Preheat oven to 400 degrees F (200 degrees C). Lightly flour a 9×5 loaf pan.
In a large bowl, combine the whole wheat flour, all-purpose flour, bran, baking soda, and salt; cut in the butter with a pastry blender until the pea sized pieces form. In a small bowl, whisk together the yogurt, milk, and mayonnaise. Stir the yogurt into the flour until just mixed. Pour into the prepared pan.
Bake for 45 to 50 minutes in the preheated oven, until golden.