In a small bowl, combine coconut milk, 2 tablespoons honey, and vanilla extract. Set aside.
Add strawberries and 2 teaspoons honey to the pitcher of a blender or to a food processor. Puree. Transfer poureed strawberries to a bowl and rinse out the blender.
Add blueberries and 2 teaspoons honey to the blender or food processor and puree.
Alternating in 3-5 layers, pour coconut mix, pureed strawberries, and pureed blueberries into 3-ounce ice pop molds (these are my favorite). Use a skewer or chopstick to blend and swirl layers slightly.
Add popsicle sticks and freeze for at least 4 hours, until solid.
To remove popsicles from molds, submerge just the mold in a bowl of room temperature water for a few seconds until popsicles easily slide out. Serve immediately.