Joseph Covenant was the patriarch of the Covenant family.
He was described by Evaline in a letter as distant and reclusive, often more focused on his books than on family. It can perhaps be assumed from his own letter that he did care for his wife and children.
He appears to have had some knowledge of the occult as it was one of his books that Jeremiah used at the Standing Stones and there are references to a spell that he prepared to help protect his family.
Joseph died seven years before the start of the game (according to one of the staff at the Manor.) Originally his son Ambrose tried to pass this off as a natural/accidental death, claiming his father had collapsed and hit his head.