Preheat oven to 350°.
For Filling: butter a 9x13-inch baking dish. Peel and core apples. Cut into thin slices. Place apples in prepared baking dish. Top with blackberries. (If using frozen berries, do not thaw first.) Sprinkle with sugar and flour.
For Topping: combine all ingredients in a small bowl until crumbly.
Sprinkle topping evenly over filling. Bake until fruit is soft and bubbly and topping is browned, about 35 to 40 minutes. Serve warm, topped with vanilla ice cream or whipped cream.