We establish the deterministic-code capacity region of a network with one transmitter and two receivers: an ordinary receiver and a robust receiver. The channel to the ordinary receiver is a given (known) discrete memoryless channel, whereas the channel to the robust receiver is an arbitrarily varying channel. Both receivers are required to decode the common message (the better-protected message), whereas only the ordinary receiver is required to decode the private message (the less-protected message). As in the single-user case, under the appropriate compactness and convexity conditions, the capacity region is either empty or else the intersection of the capacity regions of the broadcast channels that the various states induce.