Houichirou Hazuki is the current patriarch, and the Kirihito family is a branch family of theirs.
The Hazuki family is the eighth family of the Duodecim. Like the other families making up the Duodecim, the Hazuki have rules, traditions, and values unique to them, but the quality they value most is pure strength. The current patriarch, Houichirou, is a man of incredible power who values it above all else; the current matriarch, Rin Hazuki, is a rare Vision user. Houichirou's pursuit of strength for his house causes him to issue constant "exercises" for his daughter, Mai Natsume, including sending two assassins after her during her days in the Military Academy. There is, to some extent, a degree of love between the family members. However, love itself isn't permitted for an heir, and neither is freedom to some extent.  How they interact with the other Duodecim is unknown.
The family owns a sizeable estate that includes a large manor and training grounds suspended over a river. The Hazuki's also employ at least four maids to tend to their family home, one of which is Julian.
The Kirihito are a branch family of the Hazuki's, and like the Mutsuki's Kohaku family, they are trained in assassination techniques. The branch family trains their members from a young age through a harsh regime to create perfect killers. They mainly employ poisons designed to create amnesia in targets. Members of the Hazuki family take the same training and receive tutelage in the Kirihito fighting style. Even though the Kirihito family is not well-known, they do receive assassination requests like the one to assassinate Jin Kisaragi from certain members of the Kisaragi family.  The Hazukis have also hired assassins in the past, including Chachakaka.
|Mai Natsume / Another Dark Mai
BlazBlue: Central Fiction Library Entry
- Hazuki Family
One of the families of the Duodecim. ‘Hazuki' means ‘the eighth moon.' 
- BlazBlue: Remix Heart, Chapter 18
- BlazBlue: Remix Heart, Chapter 19
- BlazBlue: Central Fiction, Library Mode, Organization #008