No mention has ever been made of the parents of Avatars at all. It might be that the air nomads never knew their parents or it may just be that the Avatar is separated from them. Since Aang was our only real airbender viewpoint, we can't compare.
Starting to think we need an Avatar Fan Club thread
BonzaiBannana: A giant loophole to pubic safety
Yess! We must have Fan Club!!!