Preheat the oven to 375 degrees. Grease or line a 9-inch square baking pan with parchment paper. Set aside.
In a large bowl, stir together the sugar, cornstarch and lime juice. Carefully stir in the blueberries and raspberries. Set aside.
In a large bowl, beat together the butter, sugar, vanilla, lime zest and salt, until creamed. Slowly mix in the flour until combined and the dough starts to turn into a ball. Evenly distribute the dough over bottom of prepared pan and press lightly to hold in place. Spread the berry mixture over the bottom crust.
In a medium bowl, combine the flour, cinnamon, sugar and salt. Use a pastry cutter or your fingers to cut in butter until mixture forms coarse crumbs. Sprinkle the topping evenly over the berry mixture and bake for 50-55 minutes, or until the top is a light golden brown.
Remove from the oven and allow to cool for 30 minutes on a wire rack. Transfer to the refrigerator to chill for 2 hours before cutting into bars (otherwise it will get messy).
Store in an airtight container in the refrigerator for up to 5 days. You can freeze these bars as well for up to two months, letting them come to room temperature before serving.