Clean the mulberries thoroughly and remove any stems. For wild-harvested mulberries, soak briefly in cold water with a tablespoon of vinegar to remove any insects. Blend mulberries with 1½ tablespoons of honey until smooth. For a smoother texture, pass through a fine-mesh sieve to remove seeds (optional).
Hull the strawberries and blend with the remaining 1½ tablespoons of honey and lemon juice. The acid in the lemon juice brightens the flavor while preserving the vibrant red color.
In a separate bowl, combine the Greek yogurt with vanilla extract and a pinch of salt.
Alternate spoonfuls of the mulberry puree, strawberry puree, and yogurt mixture into popsicle molds, using approximately 1 tablespoon of each per layer. For a more defined swirl, gently run a skewer or knife through the layers.
Insert popsicle sticks and freeze for at least 4 hours, preferably overnight. If your popsicle molds don't include sticks with holders, cover the molds with foil and insert sticks through the foil to keep them upright during freezing.
To unmold, run warm water over the outside of the mold for 15-30 seconds before gently pulling the popsicles out.