1. In a blender, purée blueberries and blackberries until smooth. Pour mixture into a fine-mesh strainer set over a medium bowl to strain out seeds.
2. Rinse out blender and blend vanilla ice cream and milk until smooth.
3. Add alternating spoonfuls of ice cream and berry mixtures to 6 ice pop molds. With skewer, gently swirl. Insert 6 ice pop sticks and freeze about 4 hours, until solid. When ready to eat, run the pops under warm water for a few seconds to release from molds.