Preheat oven to 350°.
Melt 2 tablespoons butter in a 10-inch cast-iron skillet over medium-heat; sprinkle brown sugar into pan. Remove from heat. Place 1 peach half, cut side up, in center of pan; arrange remaining peach halves around center peach half. Arrange cherry halves, cut sides up, around peach halves. Set pan aside.
Lightly spoon flours into dry measuring cups; level with a knife. Combine flours, baking powder, and salt; stir with a whisk. Place granulated sugar, cream cheese, and 3 tablespoons butter in a large bowl; beat with a mixer at medium speed 3 minutes. Add egg and egg white; beat well. Add flour mixture to egg mixture alternately with juice, beginning and ending with flour mixture; mix well after each addition. Stir in the vanilla. Spoon batter into center of prepared pan; gently spread batter to cover fruit.
Bake at 350° for 35 minutes or until cake springs back when lightly touched in the center. Cool in pan 10 minutes on a wire rack. Run a knife around edge of cake. Place a plate upside down on top of pan; invert onto plate. Let stand 2 minutes before removing pan. Serve warm.