Blend all the ingredients for the banana layer together in a food processor. Pour evenly into 8 popsicle molds.
Blend the ingredients for the strawberry layer in a food processor, and pour evenly on top of the banana layer.
Use a dull knife or wooden skewer to swirl the banana and strawberry layers together.
Place in the freezer for 4 to 6 hours. If your popsicle mold doesn't come with sticks, you can insert wooden sticks after the first hour or so of freezing (so the sticks won't fall over)