So you are talking about the "Miles & More MasterCard - Companion Ticket", nothing to do with being SEN or a Companion Award.....
It quite clear from the T&C's that this will "only" get you a free (base) fare for an economy ticket when buying one for yourself.
So if you both want to travel in C, pay the difference (if they let you) or use miles and the companion award. No real other choices.