In a blender, puree the bananas with the yogurt, 2 tablespoons of the honey and the vanilla. Transfer 1 1/2 cups of the banana smoothie to a medium bowl. Add the berries and the remaining 2 tablespoons of honey to the blender and puree with the remaining banana smoothie. Spoon 2 tablespoons of the banana smoothie into the bottom of ten 3-ounce ice pop molds. Top with 2 tablespoons of the berry smoothie, then add the remaining banana smoothie. Using a skewer, lightly swirl the layers for a marbled effect. Insert the sticks and freeze until very firm, about 4 hours.