Place raspberries in a blender or food processor. Cover and blend or process until smooth. Transfer to a small bowl. Cut up the strawberries and add to same blender or food processor. Cover and blend or process until smooth. Combine with pureed raspberries. Using a fine - mesh strainer, sieve berries; discard seeds.
In large saucepan whisk together egg yolks and sugar. Whisk in milk, whipping cream and pureed berries. Cook and stir over medium heat until mixture just coats a metal spoon. Remove from heat. Stir in vanilla and, if desired, red food coloring.
Cover surface of custard mixture with plastic wrap. Refrigerate until mixture is completely chilled (4 to 24 hours) before freezing.
Freeze custard mixture in a 4 to 5 quart ice cream freezer according to manufacturer's directions. Ripen according to manufacturer's directions, if desired. Makes about 2 quarts or 16 (1/2 - cup servings).