Orford Umbridge married Muggle Ellen Cracknell and they had two children, a daughter Dolores and a son who was born a Squib. The marriage was not a happy one and both Orford and Dolores would blame Ellen as the cause of Dolores' squib brother. When Dolores was fifteen, Orford and Ellen separated and Orford took their daughter to live with him while Ellen took their son and disappeared into the Muggle world. He would never see his wife or son again.
Orford worked at the Ministry of Magic in the Department of Magical Maintenance where he would most often mop the floors. His unambitious attitude towards his career was a source of irritation for his daughter as she began her own career and rose through the Ministry's ranks. He was so despised by his own daughter that by the time Dolores was promoted to the head of the Improper Use of Magic Office, she was able to persuade him to take an early retirement. She then promised him a small financial allowance in exchange that he quietly disappear out of public sight.
Whenever people asked her if she is related to the Umbridge who used to mop floors in the Ministry, she would use her sweetest smile (which indicates her suppressed rage) to deny all connections, and falsely claimed that her deceased father was an esteemed member of the Wizengamot. Nasty things tend to happen to people who ask about Orford, or anything else Dolores did not want to talk about, so people who wished to be on her good side would pretend to believe her false heritage.
Whether or not Dolores kept her promise with her father in the small allowance is unknown, but she wanted to sever all ties with him to give herself a better image; the two clearly have little to no contact as a result. With Dolores arrested for her crimes involving the Muggle-Born Registration Commission, Orford definitely lost his pittance (assuming he is still alive at the time).
Personality and traits
Orford was an unambitious man who was content with his career as a janitor, mostly mopping floors in the Ministry of Magic. His lack of motivation allowed him to be pressured by his daughter into taking an early retirement in exchange for a small monthly allowance, leaving public sight without any commotions. He seemed to be unaware or tolerant of how his daughter would deny any connections with him, as she would falsely claim her father has died as a distinguished member of the Wizengamot.
Orford seems to have mixed feelings for Muggles as he was tolerant to marry a Muggle woman, Ellen Cracknell, but blamed her heritage for being the cause of their son to be a Squib. Finding shame in his son's lack of magical abilities, it caused his marriage with Ellen to deteriorate and eventually they divorced, with the magical and non-magical sides leaving each other, never again to cross paths.
Orford's first child and only daughter Dolores Umbridge was born with magical powers; hence he took custody of her when he divorced his Muggle wife. However, while Orford possesses magical lineage (while Dolores detests Ellen for being a Muggle), his daughter still despises him for his unambitious personality towards his own career as a janitorial employee of the Ministry of Magic. Dolores found Orford to be a source of embarrassment while she was climbing the ranks of the Ministry, and bribed him into taking an early retirement so he can quietly drop out of public sight. Dolores callously denied all connections to Orford Umbridge and instead invented a deceased father of an esteemed career. Orford was either unaware or tolerant of how his daughter shunned him aside, as he accepted her small, monthly allowance in exchange for his absence from public.
What attracted Orford to Ellen Cracknell is unknown, but their relationship was strained and unhappy after marriage. After their son was discovered to be a Squib, Orford would blame his wife's Muggle heritage as the cause of it. Tensions reached a head when Dolores reached 15 years old, and the two divorced, never again seeing each other.
Orford stopped loving his son after discovering the boy was a Squib and often looked down on him while blaming Ellen for being the cause. When the couple divorced, the boy went with Ellen back into the Muggle world, and Orford never saw his son again.
Notes and references