Charles Helliwell's Answer:
The most illuminating observation you have made is that your 'Big Boss' believes that you harbour a negative attitude towards him, and this leads me to suspect that he may be secretly trying to exert unfair and unreasonable pressure on you in the hope that you will either slip up spectacularly; or just quit.
You have already given him an opening in telling him that you would prefer that he didn't discuss issues relating to you of a personal and personnel matter, in public and in the open. He will continue to do so, in the hope that this causes you stress and anxiety and that you will slip up in some way.
Be prepared that each time he does so, he's going to try and pass it off with some ingenuous apology or a back-handed comment that you shouldn't be so sensitive; particularly in your role as potentially acting for your supervisor who is on maternity leave. This will give him the excuse to bring in someone else on the basis that he believes you are unsuitable in that role or in any future role in his team.
This is the very real and potential scenario which you may be faced with; so you really have very little choice but to present your case to HR and at least go on record as having reported him. That way, you will at very least, have given yourself some form of employment protection, which is important.
Now, as to what you should do ?
The first thing to do is to make an appointment with the Head of HR and not some junior. The reason for this is that the behaviour of the 'Big Boss' potentially crosses the line of liability on two fronts. Firstly, by contravening the normal and expected day-to-day behaviour which the company should expect from its managers, when dealing with members of staff; and secondly, and perhaps more importantly, by compromising the integrity of the company itself.
Managers, are, after all, officers and representatives of the organisations they work for and are bound by a set of practices which represent the values of their organisations. Your manager is behaving in an unreasonable and unethical manner on both fronts, and therefore it is your duty to blow the whistle on him, not only for your sake, but for the company's sake.
Hence the reason why you should share these concerns with the most senior officer in HR and not just some low level staffer. These are, potentially, very serious discretions, which might adversely affect your organisation as a whole.
Consequently, your approach has to be one where you are discussing this not just because of the effect it is having on you, but because of the potential for longer-term liability which will affect the organisation as a whole.
Of course, HR, as is so often the case, may choose to do nothing about it and just sit on their hands. However, you will have at least raised it; recorded it and got it on-the-record and that means, following this up in writing.
In the longer term, this may not save you from this manager and you may have to move to another department or another organisation; but you will have at least put down a marker, which will give you some protection and that, in itself, may be enough.
In the meantime, and for your own protection and self-preservation, you must start to keep a written record of every time an incident with your manager occurs.