Preheat the oven to 400º F and lightly grease a baking sheet with cooking spray. Set aside.
In a large bowl, combine the strawberries, rhubarb, lemon zest and juice, sugar, salt, and balsamic vinegar. Stir to combine and transfer to the prepared baking dish.
Roast in the oven for 15 minutes until the fruit is very tender. Remove from the oven and allow the fruit to cool completely.
Once the fruit has cooled, blend it at high-speed in a blender or food processor until blended but still chunky.
Put the fruit mixture into a bowl and add the yogurt mixture. Swirl the mix together with a spatula. Don't blend thoroughly. Spoon into molds. Alternatively, layer the popsicle molds with 1 tablespoon of the roasted fruit mixture followed by 1 tablespoon of the yogurt mixture until the molds are full. *No need to freeze in between layers.
Insert popsicle sticks (or tops) into the molds and freeze until solid, about 4 hours.