Bring berries and honey to a boil. Reduce heat; simmer 5 minutes. Strain mixture into a bowl, using a spoon to squeeze out juice and pulp. Discard solids. Cover and chill 30 minutes. Process yogurt and banana in a blender; pour into pop molds, alternating with berry mixture. Top with lid, and insert craft sticks. Freeze.
If you don't have frozen pop molds, you can use 2-ounce paper or plastic cups.