Mix together the orange juice, zest, and 2/3 cup of the sugar until they are completely combined. Using a whisk or hand mixer, whip the heavy cream and remaining sugar until the cream is thick and forms soft peaks. Stir the milk into the orange mixture. Gently fold the heavy cream into the orange mixture. Refrigerate your sherbet base for at least one hour and then churn according to the directions of your ice cream maker. When the sherbet comes out of the ice cream maker, it will have the texture of soft-serve ice cream.