In a blender or food processor, combine the raspberries, raspberry vinegar and 1 1/2 tablespoons of the tarragon; season with salt and pepper and blend until pureed. With the machine on, add the olive oil in a steady stream.
In a large bowl, toss the red and green cabbages together; add the vinaigrette and toss to coat. Season with salt and pepper and refrigerate for at least 1 hour or up to 4 hours. Just before serving, stir in the remaining 1 1/2 tablespoons tarragon.