Make crust: Preheat oven to 400°F. In a bowl, mix flour and salt. With a pastry blender or two knives, cut in butter and shortening until crumbly. Sprinkle with 3 Tbsp. ice water; mix with a fork just until dough forms a ball (add water if needed). Form into a disk, wrap in plastic and chill for 30 minutes. On a floured surface, roll out into an 11-inch round. Fit into a 9-inch pie pan and crimp edge. Refrigerate for 10 minutes.
Line crust with foil and fill with pie weights. Bake for 6 minutes, remove foil and bake until lightly golden, 10 to 12 minutes. Let cool.
Make filling: In a bowl, beat cream cheese and sugar with a mixer on high speed. Beat in cream and vanilla, scraping down sides of bowl, until fluffy and well-mixed. In another bowl, gently mix berries.
Spoon two-thirds of cream mixture into crust; smooth top. Spoon two-thirds of berries over cream. Mound remaining cream in center and top with remaining berries. Chill for 1 to 4 hours.