The Imperial Family at any point in time is the House and Dynasty of the standing Emperor.
The formal custom is that the Emperor, Empress, and their issue officially compromise the immediate Imperial Family. By extension the Noble House and extended relatives of the standing Emperor are also accorded certain privileges. The privileges of the second cousins of a standing Emperor have been successfully challenged in the past.
There has not been a non-human Emperor to date although many conjecture that one day there will be one. Imperial legal scholars have adopted the convention that if a sophont Emperor of a species with genders other than male and female assumes the Iridium Throne, the default title will be Emperor.
History & Background (Dossier)
When the first Emperor, Cleon I, of the Third Imperium seized power, a precedent was set that the Imperial Family would possess a number of rights, most held by custom and tradition rather than by code of law. Many of the hereditary (monarchical) features of Imperial rulership of the Third Imperium are not codified, part of a careful compromise with the Moot and greater standing body of Imperial Nobility. This compromise and system developed over a millenium of rulers as the Third Imperium grew and developed.