There's no explanation given as to the nature of their relationship or how this scenario came to be (other than a simple "she started behaving this way some time ago yadayada"). Judging by how they address each other, they're not related. But not married or lovers either (something he also states somewhere, not sure if that was part of the pet play though) as he uses her last name, which I would consider too formal for a couple (which is also a sign that they are not related btw)
On the last page she's just asking him to come again tomorrow. So I guess they're not exactly living together, as the name plate reveals. (only her name at the door)