The best expression I found is here:

The normal definition of a cuckold is a married man whose wife cheats on him with or without his knowledge. A cuckold fetishist is aware of his partner's activity and derives sexual pleasure from it.[3] In this subculture, the female is typically sexually dominant, while the male takes on a submissive role, only becoming involved with her or her partner when she permits it—sometimes remaining altogether celibate. Other arrangements are certainly possible, however.

The desire for the male to enjoy being cuckolded is more related to sexual gratification and less about interpersonal ideals (respect, commisary, between the partners). Sometimes this is part of the their sexual fantasy because they gain sexual arousal through being humiliated. Other times the husband finds pleasure through that of his wife. In a broader context, the contrast between a cuckold and the additional male participant is sometimes used to summarize an individual's personality or behavior and the variability commonly seen in male libidos: the cuckold or beta male suggesting a lack of masculinity or alpha male representing that missing masculinity.

The wife and extramarital participant may both enjoy attempting to actively include him in the act of cuckolding as much as possible through serving her. Some common themes include praising her appearance, attempting to stimulate her sexually at the same time as the additional participant, and generally being engrossed in her enjoyment. It is common for the male to be more absorbed with the female's pleasure than his own.

The wife who enjoys cuckoldry is sometimes referred to as a hotwife or cuckoldress.