Preheat oven to 325°with a rack in the lower third.
Place six 4oz. ramekins in a medium roasting pan; set aside.
In a medium saucepan add milk, milk chocolate and bittersweet chocolate over medium heat.
Bring almost to a simmer; remove from the heat. Set aside, stirring occasionally, until chocolate is melted.
In a medium bowl, whisk together egg yolks, sugar, and salt. While whisking, add a little of the hot milk mixture to the egg mixture to combine. Add the remaining milk mixture, and whisk to combine.
Whisk in vanilla. Fold in yogurt.
Strain through a fine-mesh sieve into a large liquid measure.
Pour approximately 1/2 cup of the mixture into each ramekin.
Transfer the roasting pan to the oven.
Fill pan with enough boiling water to come halfway up the sides of the ramekins.
Bake until the custards are just set in the center, about 35 minutes.
Remove the roasting pan from oven.
Remove the ramekins from the water, and place on a wire rack to cool.
When completely cooled, cover, and transfer to refrigerator.
Chill for at least 4 hours and up to overnight.
Serve with a dollop of whipped cream, if desired.