Drain off any excess liquid from the yogurt containers to ensure a creamy consistency. In a large mixing bowl, combine the plain yogurt, Greek yogurt, sugar, and honey. Whisk vigorously until the sugar is fully dissolved, creating a smooth and uniform mixture. Taste the blend, and if the tartness is too pronounced, incorporate additional sugar or honey to balance the flavor.

Prepare your frozen yogurt using an ice cream or frozen yogurt maker, following the device's specific guidelines. Allow the mixture to churn until it reaches a thick, smooth, and firm consistency, signaling that it's ready. Keep in mind, the texture will firm up further when placed in the freezer.

Serve the frozen yogurt immediately, topped with fresh fruit or any desired toppings. Alternatively, transfer it into an airtight container for freezing. If stored for an extended period, let the frozen yogurt sit at room temperature briefly to soften before serving for the best texture and taste.