The House of Joseph (or simply, Joseph) is the term for the collective descendants of Joseph, the two tribes of Ephraim and Manasseh. In the vast majority of places in the Bible, Ephraim and Manasseh are considered their own seperate tribes; inconsistent with the other tribes which are each descended from one son of Jacob. This is due to Jacob giving a special blessing to Ephraim and Manasseh separately.
In certain circumstances, the entire family line that descended from Joseph was considered as a whole, rather than as two separate tribes oftentimes with the phrase, "House of Joseph", the "sons of Joseph", the "people of Joseph" or simply "Joseph" (and many other terms). Oftentimes this would be used as a descriptive phrase of Ephraim and Manasseh or would be used without reference to the two "half-tribes". The House of Joseph was used in special circumstances in genealogy, blessings, legal records and historical depiction to show the common ancestry and inheritance of the two tribes of Joseph.
The Seed of Joseph
Birth of Ephraim and Manasseh
Joseph being the firstborn of Jacob's favorite wife (Rachel) was ostracized by his brothers. Originally scheming to kill Joseph, Joseph was sent off to Egypt-- not to be seen again by his family for at least a decade. During this time, Joseph ascended the ranks of the Egyptian government, despite many setbacks. Under the name, Zaphnath-Paaneah, Joseph became one of the highest ranking officials in the government (whether or not he was the vizier is difficult to determine) and received the hand of Asenath the daughter of On's (Heliopolis') priest, Potiphera in marriage.
Prior to the famine in Egypt, Joseph had two sons by Asenath: Manasseh the firstborn and Ephraim, alongside any daughters he may have had.
The Sons' Blessings
After settling with his extended family in the land of Goshen, Joseph's father became ill.