The "faithful party" refers to the members of the crew of the Hispaniola who can be trusted not to side with the pirates. Not counting Jim, since he is a boy, there are six men in the faithful crew, compared to the mutineer's nineteen (as stated on the last page of Chapter 12).
In Chapter 11, Jim is fortunate enough to overhear Long John Silver, who is ostensibly the ship's cook, conversing with other crewmen and eliciting their plans for a mutiny at a time of Silver's choosing. Silver would prefer to let Captain Smollett, a capable if annoying seaman, to do most of the work for them, since they lack anyone among their number with skill in navigation. Silver has evidently been able to convince some of the crewmen who were not originally part of Flint's crew, and therefore familiar with Silver and his plan, to join up with them anyway, casting doubt on the reliability of almost everyone on the ship.
When Jim relays this information to Trelawney, Smollett, and Livesey, they determine they can only trust themselves, Jim, and the men they brought on board with them.