In a small saucepan, combine the strawberries, raspberries, 1/4 cup sugar and a pinch of salt. Bring to a simmer over medium heat, stirring, and cook until jam like, about 10 minutes. Let cool, cover and refrigerate until cold, about 1 hour.
In a medium bowl, whisk together the cream, milk, remaining 1/4 cup sugar and another pinch of salt until the sugar is dissolved; cover and refrigerate for 1 hour.
Using an ice cream machine, process the cream mixture according to the manufacturers instructions. Fold in the chilled berry mixture to make a swirl pattern and then transfer to an airtight container. Freeze until firm, about 4 hours.
