Heat oven to 400. Peel peaches and slice. Combine them with 3/4 cup of sugar, the cornstarch and lemon juice. Gently stir in raspberries. Transfer to 2-qt. baking dish. Cover with foil.
Bake until juices are bubbling, about 30 minutes. Meanwhile, combine 1/4 cup sugar, flour, baking powder and salt. Cut in butter until mixture resembles coarse meal. Stir milk into flour mixture until ingredients just hold together. Drop eight heaping spoonfuls of dough onto hot fruit and sprinkle remaining sugar on dough. Bake, uncovered, until the biscuits have browned, about 25 minutes.