I think passive-aggressive behaviour can be a characteristic associated with various personality disorder, but all kinds of people do this without being considered mentally ill.
In my experience, it takes a lot of cultivation of self-awareness for the person to recognise when they're doing it and why, which takes education and counselling usually. There are all kinds of payoffs involved in p/a behaviour and the person needs to find alternative ways of getting those if they are going to leave behind the p/a way of dealing with things.
However, passive-aggressive behaviour is just one side of a dynamic with others. How others respond to the behaviour can feed into that dynamic, too. It's easy to feel compelled to respond to p/a behaviour out of guilt, shame, fear, obligation, etc., which should be addressed as much as the p/a behaviour.
Hope that helps.
TheOneInFour