For Balthier, family is very mildly discussed, and has remained a mystery for a large portion of the game. Because of the conditions, not very much is known about his family outside the game itself.
Balthier's father, Doctor cidolfus Demen Bunansa, as presented by the game. Balthier first brings up the fact that he's his father upon the party's arrival at Phon Coast. One of the only people to address him by his real name nowadays, Cid is anything but the ideal father. Emotionally torn from watching his father being eat away by his own ambition, Balthier left his former life behind him. Because I am unwilling to retell the story (read: lazy!) of Balthier's history with his father, you may find the details and such of it here.
According to the timeline in Final Fantasy XII: Ultimania Omega, it is noted that Balthier is the third son of Doctor Cidolfus Bunansa, meaning he has two other brothers whose birth preceeded his. The game does not make any mention of the older brothers Balthier has, so it's assumed that their significance in Balthier's past seems irrelevant. However, this does clear up a few mysteries: for one, he is not an only child. Secondly, Balthier would be the sole "prodigial" son of his siblings; the timeline mentions that Cid gave up on his son and turned to Vayne instead, not to any of his other children. Additionally, any sisters or younger brothers that Balthier might have is not noted anywhere. Nevertheless, siblings of a few characters were also not brought up in the game, such as Penelo's brother, who died during the war, or Ashe's eight (possibly more) other siblings!
Final Fantasy Tactics presents a playable minor character by the name of Mustadio Bunanza. Although there is no confirmed connection to Balthier himself, the similarities are almost uncanny. Both characters weild a gun and seem to share an interest in the mechanics of airships; the only difference in their interests are that guns and airships are of ancient relics in FFT. Although there is a slight difference in spelling between their surnames, the original katakana spelling is identical:
Famran Mid Bunansa: ファムラン・ミド・ブナンザ (romaji: Famuran Mido Bunanza)
As stated in the timeline, Tactics takes place several years after the events of Final Fantasy XII. Since both games share the same world, it's safe to say that any blood relation from Mustadio to Balthier is anything but impossible.