MAKE THE MOJITO LAYER: In a blender, puree all of the ingredients except the xanthan gum on high speed until smooth and bright green, about 30 seconds. Pour into a bowl.
Slowly sprinkle the xanthan gum over while quickly whisking, until slightly thickened and foamy. Let rest for 15 minutes, then skim any foam.
Pour 1 1/2 tablespoons of the mojito layer into eight 3-ounce popsicle molds or paper cups. Freeze until almost firm, 1 hour. Poke a popsicle stick into the center of each.
MAKE THE WATERMELON LAYER: In another bowl, combine all of the ingredients except the xanthan gum.
Slowly sprinkle the xanthan gum over while quickly whisking, until slightly thickened. Let rest, then skim.
Carefully add 1 1/2 tablespoons of the watermelon layer to the mojito layer in the molds. Freeze until almost firm, 1 hour.
Pour the remaining mojito mixture on top and freeze until almost firm, 1 hour.
Top with the remaining watermelon layer and freeze until firm, 2 hours. Unmold and serve.
NOTES: The thickening agent xanthan gum is available at many supermarkets and on amazon.com. Simple Syrup: In a saucepan, simmer 4 ounces of water with 1/2 cup of sugar over moderate heat, stirring, until the sugar dissolves, about 3 minutes; let cool. Refrigerate for up to 1 month. Makes about 6 ounces.