Make the Red Layer: In a blender, combine the strawberries, sugar and lime juice. Puree, scraping down sides as needed. Pour through a fine-mesh sieve into a bowl, pressing on solids; discard solids. Fill the ice-pop molds 1/3 of the way (you may have some strawberry puree leftover). Freeze until firm, about 30 minutes.
Make the White Layer: Whisk together the yogurt, cream, sugar and lime juice in a small bowl. Remove the molds from the freezer and top with the yogurt mixture, filling each another 1/3 of the way. Freeze until firm, about 30 minutes.
Make the Blue Layer: In a clean blender, puree the blueberries, sugar and lime juice. Puree, scraping down sides as needed. Pour through a fine-mesh sieve into a bowl, pressing on solids; discard solids. Remove molds from freezer; insert popsicle sticks through the white layer. Top with the blueberry puree (again, you may have some leftover puree), leaving ¼-inch of free space at the top of the molds. Freeze until solid, 3 hours or more (or up to 1 week). Just before serving, briefly run molds under hot water to release the pops.