In a medium saucepan, combine heavy cream, milk, and granulated sugar over medium heat. Stir continuously for 5 to 7 minutes until the sugar dissolves and the mixture is warm but not boiling. Remove from heat, then stir in vanilla extract. Allow to cool completely at room temperature.

In a blender, combine fresh or thawed raspberries with a bit of sugar, then blend until smooth. Strain through a fine-mesh strainer to remove seeds.

Pour the cooled mixture into your ice cream maker. Churn according to the manufacturer's instructions until it reaches a soft-serve consistency, about 20 to 25 minutes.

Divide churned base into three parts. For orange, mix one part with orange juice and zest. For lime, mix lime juice and green food coloring. For raspberry, mix with the raspberry puree.

In a freezer-safe container, alternate spoonfuls of each flavor, swirling gently with a spatula. Cover and freeze for 4 to 6 hours until firm.