Preheat the oven to 350 degrees F (175 degrees C). Grease a deep 9-inch pie plate.
Whisk all-purpose flour, almond flour, baking powder, and salt together in a medium bowl.
Whisk ricotta cheese and milk together in a small bowl until smooth.
Beat butter with an electric mixer until creamy. Add sugar and beat until very light, about 3 minutes. Add vanilla and almond extracts; beat until blended. Scrape down sides with a spatula. Add eggs one at a time, beating well after each addition.
Alternate adding flour mixture and ricotta mixture to the batter, beating briefly between additions. Scrape down the sides of the bowl.
Pour batter into the prepared baking dish. Smooth the top with the spatula. Sprinkle strawberries and blueberries over the top. Press very gently into the batter. Sprinkle turbinado sugar on top.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 70 minutes. Cover with foil when top starts to brown. Cool completely on a rack before slicing.
