1. Combine the blackberries, blueberries, lime zest and juice, and maple syrup in a medium bowl.
2. Preheat oven to 375° with rack in center. Grease a baking sheet. In large bowl, whisk together the flour, cornmeal, sugar, baking powder, and salt. With fork, work butter into flour mixture until it resembles coarse meal. Add buttermilk, tossing with fork just until dough begins to hold together.
3. Transfer dough to prepared baking sheet; pat into a 7- to 8-inch circle. Bake until golden brown (about 30 minutes).
4. Let the cornmeal shortcake cool slightly. Split horizontally and spread bottom layer with yogurt. Spoon berries and their juices over yogurt, reserving a few berries for top. Cover with shortcake top and sprinkle with reserved berries. To serve, cut into 6 wedges.