To make berry filling: Combine raspberries, blackberries, sugar and framboise (or kirsch) in a bowl. Let stand at room temperature, stirring occasionally, for 30 minutes to 1 hour.
To make & assemble shortcakes: Preheat oven to 425 °F. Lightly oil a baking sheet or coat it with nonstick spray.
Whisk all-purpose and cake flours, 1/4 cup sugar, baking powder, baking soda and salt in a mixing bowl. Cut cream cheese into dry ingredients using a pastry blender or your fingers until mixture resembles coarse meal.
Combine 3/4 cup buttermilk, oil and vanilla in a glass measuring cup. Make a well in the dry ingredients. Add wet ingredients and stir with a fork until just combined. (Dough will be slightly sticky; do not overmix.)
Turn dough out onto a lightly floured surface. Gently pat into a 3/4-inch-thick circle. With a floured 3- or 3 1/2-inch cutter, cut out shortcakes and place on prepared baking sheet. Press dough scraps together and repeat to make 8 shortcakes.
Brush shortcake tops with remaining 2 tablespoons buttermilk and sprinkle with remaining 1 tablespoon sugar.
Bake shortcakes for 10 to 12 minutes, or until light golden. Transfer to a wire rack to cool slightly.
To serve, split shortcakes in half with a serrated knife. Set bottoms on dessert plates. Spoon on berry filling and vanilla sauce. Set tops on at an angle. Serve immediately.