In Battlefield Heroes there are only two factions, the Royal Army and the National Army. The Royals are based off a cross between the Americans and British from World War II while the Nationals reflect the Germans.
According to its own fictional history, Royals and Nationals were once great friends. The current conflict started during the Olympics when the Royal Nation accused the National Homeland of cheating during a track cycling contest. Controversy arose and the Nationals made fun of the Royal's King moustache, which lead the Royals to declare war against the Nationals, to which they have a mutual conflicting history from ages past.
Neither faction has any inherent weaponary or ability advantage over the other, though some argue some maps slightly favour one team, with the initial two bases the players capture generally depending on their faction. These slight issues arise due to a lack of symmetry on Battlefield Heroes maps.
Speculations about a third Faction are quite rare and not reasonable because the game is based on the war between them. From Matchmaking over till the battlefields all is created for only 2 Factions.