Combine first 3 ingredients in container of an electric blender; cover and process until smooth, stopping once to scrape down sides.
Place berry mixture in a wire-mesh strainer; press with back of spoon against the sides of the strainer to squeeze out juice. Discard pulp and seeds remaining in strainer. Add sugar, buttermilk, cream, and orange juice to strained mixture; stir well.
Pour mixture into freezer container of a 1-gallon hand-turned or electric freezer. Freeze according to manufacturer's instructions. Pack freezer with additional ice and rock salt, and let stand 1 hour before serving. Garnish with fresh berries, if desired.