Carter, where have you been counselor? Happy New Year and it's good to see your thoughts again. Don't kill me for the billable hours harangue on the other thread!
Tee, JJ and cb nailed this one. Assistants are there for the players. Some of them are nice and want to make your life easier, but tehy are usually the exception rather than the rule. Like a co-worker who gives you a civil greeting, question or response, treat them accordingly. I usually don't let them ask questions about the game or calls. If he wants to know how my wife and children are, I may oblige and even reciprocate. In NCAA ball, those coaches may actually be able to impede your career. Some of them fill out the ratings forms and have the boss sign 'em. Even for high school ball around here, the assistant coach may be the brains behind the brawn. But, he's still the assistant and I can't remember the last time I ejected one. By the time they get up, the head coach has told them to sit down or is leading the way.
As far as the original question goes, help steer an assistant coach away from your partner. Try to head him off or get between your partner and him. If your partner knows what he is doing, he is walking away and the agressor is obvious to everyone. When both are out there barking at him, escort him away from the fray and let your partner handle the head coach. Do not put your hands on him and don't let him do that to you. You both have a job to do and the kids need a few more "that wasn't you" or "pick out a good ones".