In a blender, combine the strawberries, lime juice and 2 tablespoons honey and blend until puréed. Divide the mixture evenly between the popsicle molds and freeze until firm, about 1 hour. Clean the blender and set it aside.
In a medium bowl, whisk together the yogurt, coconut milk and remaining 3 tablespoons honey until smooth. Divide the yogurt mixture evenly among the popsicle molds, pouring it atop the frozen strawberry layer. Insert popsicle sticks into the center of each mold and freeze until firm, about 1 hour.
In a blender, combine the blueberries, pomegranate juice and lime zest and blend until puréed. Divide the blueberry mixture evenly between the popsicle molds, pouring it atop the frozen yogurt layer, and freeze until firm, a minimum of 3 hours.
When ready to serve, briefly run the popsicle molds under warm water then gently pull the popsicles from the molds and serve.