In a medium saucepan, gently heat 2 cups of heavy cream, 1 cup of whole milk, and 1 cup of granulated sugar over medium heat. Stir continuously until the sugar completely dissolves.

Allow the mixture to cool to room temperature before transferring it to the refrigerator. Chill the base for at least 2 hours, or until it's completely cold.

While the base is chilling, prepare the raspberry layer. Blend 2 cups of fresh or thawed raspberries with 1/4 cup of sugar until smooth. Strain the puree through a fine sieve, discarding the seeds.

Once your base is chilled, pour it into an ice cream maker and churn until it reaches a soft-serve consistency.

Divide the churned base into three equal parts in separate bowls. For the orange layer, mix 2/3 cup of fresh orange juice and orange zest into one part of the base. For the lime layer, use 1/3 cup of fresh lime juice and zest in another part. In the last portion, incorporate your prepared raspberry puree.

In a freezer-safe container, start spooning the orange layer followed by the lime layer, and then the raspberry layer. Alternate each flavor and lightly swirl them together.

Cover the container tightly and place it in the freezer for at least 4-6 hours, or until it becomes firm.

Before serving, let the sherbet sit at room temperature for a few minutes to soften slightly and then scoop into bowls or cones.