Hello P, J, A;
Welcome to our forum.
I've heard "thruple" used to refer to "a couple plus one;" perhaps that's what you're looking for. Otherwise "friends with benefits" seems appropriate enough. The greater the emmotional connection/entanglement/commitment, the more "polyamory" becomes a fit word for it.
Kind of stating the elephant in the room, but it seems to me that at some point, A should probably admit to his wife that he's playing with you two (P&J).
If A wants some one-on-one encounters with J, but that is causing P some jealousy issues, it's something to talk about (all three of you), to find out how important this is to A, and what can be done to make it a little easier on P. Perhaps there are some small steps that can lead up to this A+J encounter? some way of taking it slow.
That's all I have for right now; let me know if you have further questions.
Glad to have you onboard.
Love means never having to say, "Put down that meat cleaver!"