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Stephen's relationship with his daughter is obviously a good one, since in his first appearance she gave him a kiss on the cheek and told Ross that she was utterly humiliated after having said the wrong name at the altar.
Stephen has a hostile relationship with his wife, Andrea. It is revealed they have a bad marriage since they openly treat one another with disdain.
It is implied that Stephen and Ross were on civil terms with each other before the wedding took place, but after saying Rachel's name and having huge dislike of Jack and Judy Geller, Ross and Stephen become at odds with each other.
Jack and Judy Geller
Stephen strongly disliked Jack and Judy Geller after they both refused to pay for the Walthams' wine cellar. They had only one brief moment of politeness (when they first met) and then the hostility increased when Jack and Judy kept refusing to pay for the wine cellar and at the reception, when Judy asks Jack if they were bad parents, Stephen walks by and answers "Yes" causing Jack to snarl at him at who serves steak when there isn't a place to sit. Ross eventually got both parents to stop arguing on the wedding day by threatening not to have any grandchildren with Emily.
Stephen did not like Rachel at all since Ross said her name at the altar which caused him to spoil the ceremony.