Arrange the bread cubes in a shallow baking dish (about 11x7 or 13x9 inches). Arrange the dried berries all over the top.
In a large bowl, whisk together the milk, sweetened condensed milk, eggs, egg whites, vanilla extract and cinnamon. Pour the mixture all over the bread and berries. Press down to cover the bread with the milk mixture. Sprinkle the brown sugar all over the top of the bread mixture. Cover with plastic, press down slightly to cover the bread with the milk mixture. Refrigerate up to 24 hours.
Preheat the oven to 350 degrees.
Remove the plastic from the baking dish and bake the bread pudding for 45 minutes, until the top is golden brown and the milk mixture is set.
