Phineas NigellusAccording to the HP Lexicon, Phineas is Sirius's Great-Great-Grandfather. He may or may not be related to Bellatrix as it is unclear whether he was related to Sirius's father or his mother. If he was related to his father, then he is probably related to Bellatrix as well. During his life, Phineas was headmaster of Hogwarts and he currently spends his time residing in two paintings; one at Hogwarts and the other at 12 Grimmauld Place.
Mrs. Black (Bellatrix's mother)We know practically nothing about Bellatrix's mother. Without a doubt she would have been a pure-blood, however nothing more is known about her. She birthed three children; Bellatrix, Andromeda, and Narcissa.
Mr. Black (Bellatrix's father)As with Mrs. Black, we know nothing about Bellatrix's father either. He was brother to Sirius's father and was therefore a pure-blood. He had three daughters; Bellatrix, Andromeda, and Narcissa.
Andromeda Tonks (nee Black)Andromeda was middle daughter to Mr. and Mrs. Black. Her name means "the woman chained". She married Ted Tonks, a muggle, and had one daughter that we know of, Nymphadora Tonks.
Nymphadora TonksNymphadora is neice to Bellatrix and it is estimated by the HP Lexicon that she was born in 1974. She was born a Metamorphmagus which enables her to change her appearance at will. She is an Auror who works for the Ministry of Magic, and is also a member of the Order of the Phoenix. There appears to be no family commitment between Nymphadora and Bellatrix, as she was found to be badly maimed by her Aunt within the Department of Mysteries.
Narcissa Malfoy (nee Black)Narcissa is Bellatrix's sister and was probably youngest daughter of Mr. and Mrs. Black. Her name means "self-absorbed" and originates in the Greek myth of Narcissus. She married Death Eater, Lucius Malfoy, and birthed a son, Draco Malfoy.
Draco MalfoyDraco is the only child of Narcissa and Lucius Malfoy. He is nephew to Bellatrix and is currently the same age as Harry Potter. He is in Slytherin house at Hogwarts and is Harry Potter's school-yard enemy.
Mrs. Black (Sirius's mother)Mrs. Black was a pure-blood and was mother to Sirius and Regulus Black. According to the HP Lexicon she died in 1985 and currently resides at 12 Grimmauld place in a life-sized painting. She screams insults at the residents of the house whenever the curtains that hide her portrait are pulled. Although not a Death Eater herself, Mrs. Black believed strongly in Voldemort's ideals and encouraged her son (Regulus) to join the Death Eaters.
Mr. Black (Sirius's father)As with his brother and sister in law, very little is known of Mr. Black. He is the father of Sirius and Regulus Black and was married to Mrs. Black.
Sirius BlackSirius is cousin to Bellatrix and brother to Regulus. In his time at Hogwarts, he was in Gryffindor and became an unregistered animagus. Once graduated, he joined the Order of the Phoenix. During his time in the Order, he was wrongly accused of being a spy for Voldemort and was placed in Azkaban shortly after Voldemort's defeat. He escaped 13 years later in order to help protect his godson, Harry Potter. He was killed 2 years later by Bellatrix during a battle in the Department of Mysteries.
Regulus BlackRegulus was Sirius's younger brother and Bellatrix's cousin. He was "weaker" than Sirius and followed his parents pure-blood ideals, even joining the Death Eaters once he graduated. He found that he wasn't suited to life as a Death Eater but before he managed to escape, he was killed by one of his fellow Death Eaters.