The factions are as below:
High Elves, Banner Lords, Barbarians and Sacred Order
Orcs, Orgyn, Lizardmen and Skinwalkers
Dwarves
You are supposed to use champions from either of the three groups above
You forgot Demonspawn, Undead Hordes, Dark Elves, and Knight Revenant.
Each line of factions also has a name, which may appear in the special rules for events and tournaments.
Telerians, Gaellen Pact, The Corrupted, Nyresan Union. The last one only contains a single faction, Dwarves, so far.
I think the rule about the mono-faction teams is about a single faction, not a group of factions, though.