Mix the blackberries, peaches, cornstarch, and sugar in a large bowl.
Press one of the pie crusts into the bottom of a 9-inch pie pan. Pour the blackberry mixture into the pie crust. Cover with the remaining pie crust. Crimp the edges of the two crusts together to seal. Cut slits in the top of the pie to vent. Brush the top with the melted butter. Sprinkle the cinnamon and nutmeg over the top.
Bake in preheated oven for 15 minutes. Reduce the oven temperature to 350 degrees F (175 degrees C) and continue to cook until top crust is golden brown, 35 to 40 minutes.