Zest three blood oranges in a large bowl and set aside. Juice the blood oranges and 1/2 grapefruit. You will need 3 cups of juice.
In a small saucepan, heat 1 1/2 cups of the orange and grapefruit juice, sugar, and salt on medium until sugar dissolves. Remove from the heat and pour it into the bowl with the zest. Slowly stir in the remaining juice, triple sec, milk, and cream. Whisk until combined. Cover the bowl and place into the refrigerator to chill, about 30 minutes.
Once chilled, pour the mixture into an ice cream maker and freeze according to the manufacturer’s instructions. Once your sherbet is ready, scoop into a container. Place parchment directly on top of the ice cream to prevent ice crystals from forming. Cover with a lid and freeze until firm, at least 4 hours.