Pour the milk and cream into a small saucepan. Add the sugar and salt and place over medium-low heat. Heat until the sugar dissolves completely, stirring frequently. Don't let the mixture come to a boil. Transfer the base to a container and refrigerate for a few hours or overnight.
Once the base is in the fridge, blitz the raspberries in a food processor and strain them through a fine-mesh strainer. Discard the pulp and seeds and transfer the remaining puree to the fridge. Leave the raspberry puree to chill for a few hours. Strain the orange and lime juices into separate bowls and whisk in gel color, if desired. Transfer the two to the fridge and let chill alongside the base and raspberry puree.
Once the base is chilled, pour it into an ice cream maker and churn for 30 minutes or until it resembles soft serve. Divide the base into three resealable containers. Fold the lime juice into one, the orange juice into another, and the raspberry into the final container. Cover the sherbets and place in the freezer to chill for at least an hour, 2 is better.
Once the sherbets have chilled, take the sherbets and the cake pan out of the freezer. Line the base of the pan with parchment paper and add one scoop of each sherbet to the pan and top with three more scoops, taking care not to place the same flavor on top of each other. Fill the cake pan with sherbet, leaving an inch and a half of headroom at the top. Using a butter knife, swirl the flavors together but don't get too carried away. You just want to swirl them not fully integrate them. Cover the cake pan and transfer it to the freezer. Let chill for 2 hours.
Once the 2 hours have passed, place the funfetti cake on top of the sherbet and lightly press. Cover once again and let chill for at least 4 hours or overnight.