Place the honeydew into the bowl of a blender or food processor fitted with a metal blade. Process until completely pureed. Pour into a large container or bowl. Add the honey and stir. 

Place the peaches into the bowl of the blender or food processor and process until completely pureed. Use a fine mesh strainer to strain the peach puree into the container with the pureed melon. Mix well and refrigerate until serving. 

To serve, ladle the soup into shallow soup bowls. Carefully scatter the berries among the bowls so that you can still see them and they do not sink. Take a melon baller and scoop one ball each of the three sorbet flavors and carefully place into the bowls. Depending on the size of your bowls, you can add more than three sorbet balls to the bowl.