In a blender, puree all berries and a ½ cup of ice cream until smooth.
Strain mixture through a sieve over a large bowl, pressing with a spoon or rubber spatula to extract liquid. Discard seeds.
Transfer berry mixture back to blender, adding remaining 1 ½ cups ice cream, and blend until smooth.
Pour into popsicle molds and freeze until completely hardened, at least 6 hours.
Remove from molds and enjoy!