Quarter and core the radicchio and cabbage, and very thinly slice both vegetables. Halve and very thinly slice the red onion. Place the radicchio, cabbage and onions in a large bowl. Sprinkle over the orange juice, lemon juice, and balsamic vinegar and toss. Set aside for an hour, tossing every once in awhile so that the acids and salt wilt the vegetables a bit. This can also be covered and refrigerated for up to a day, tossing occasionally if possible.
In a small container, place the olive oil, honey and thyme. Shake to combine. Pour over the cabbage mixture and toss to combine. Taste and add salt and pepper as needed.