Pain in the Ass with Benefits
Two people whose relation only exists because of a sexual relationship. This may often be seen from others as "Friends with Benefits" type of situation. However, unlike that situation one of the two people is faking enjoyment of the friendship component. The person facilitating the deception is doing so in order to avoid causing a negative emotional response which may cease the sexual component.
Shirley has a Pain in the Ass with Benefits situation going on with Mike.