First, understand that the boss’s behavior is an indication that something is wrong with them, not you. Feel bad for them that they are damaged in this way because it really does effect all their relationships.
Second, start documenting and keep a paper trail. Do not have any communication with the boss that isn’t documented. Passive aggressive individuals tend to promise support for projects and then withhold it and then blame the victim for not completing their tasks. If you agree to anything verbally, follow up with an email verifying what was agreed to. Make sure that this is cc’d to another person, usually your boss’ superior. This will help create a papertrail that will come in handy and avoid the he said/she said conflicts that result from interactions with passive aggressive individuals.
Don’t get emotionally upset when this person behaves poorly. Expect them to and plan for it. This puts you in control and that feels a lot better than being at the whims of a passive aggressive boss.
How this plays out. The boss plays their normal games, everything is documented, including their promises with date and time stamps. When things go wrong, you produce the documentation. You do this very sweetly and professionally and in an effort to help correct the problem and clear up any misunderstanding because you are an eager member of the team just trying to make sure the company is successful. You don’t do this to get your boss in trouble, you just want to make sure the project is successful and you are just in the habit of documenting everything so that you don’t make a mistake or misunderstand an instruction.
There are a few possible outcomes from taking this approach. 1) the boss starts behaving better because it becomes clear they can’t play these games with you anymore (ideal – unlikely to happen). 2) it becomes clear that your boss is the problem and isn’t following up or doing what they said they will do, in which case, their bosses become alerted to the problem. 3) They become really aggressive and really obnoxious in an attempt to bully you into giving up your power over them that your documentation provides. You refuse and continue to sweetly do your job professionally and fully documented and the boss’ behavior becomes so egregious that action is taken.
The key to this is to be consistent. Document everything! And I mean everything. Don’t get mad or upset. Passive aggressive people are unhealthy and need help. You document to make sure that they don’t negatively impact you, your co-workers and the company. It’s the moral thing to do and the right thing to do and it really does work.