Place raspberries in a food processor; process until smooth. Strain raspberries through a sieve into a bowl, reserving raspberry purée. Discard solids. Combine raspberry puree, sugar, and vanilla in a large bowl. Stir in milks.
Pour mixture into the freezer can of an ice-cream freezer, and freeze according to manufacturer's instructions. Spoon ice cream into a freezer-safe container; cover and freeze 1 hour or until firm.