A "consensual relationship" refers to a relationship where both parties willingly agree and give their permission to be in that relationship. Full definition
When Robach asked Paley if her subsequent consensual relationship with Franco complicates her story, the aspiring comedy writer said, «Yes, of course. (vanityfair.com)
«We were a couple,» Martina answers truthfully, adding, «It was a healthy, consensual relationship between two adults.» (awfj.org)
Indeed, societal conditioning or not, many people seek monogamy as it's what makes them feel happy — and whichever consensual relationship makes you feel the happiest and most secure is the right relationship for you. (elitesingles.ca)