As an instructor, I'm struggling to understand what was happening during this flight. If you're recording a flight as Pu/t or dual, it is either as a part of a course for the initial issue of a licence, or the addition of another rating, or for the revalidation or renewal of a rating. In any case, you would have been briefed by your instructor prior to the departure and would either have observed, 'followed through' or actually conducted the take-off and landing. Thus the entire flight should be recorded as dual by yourself and PIC by the instructor. I really don't see how you can be adequately briefed for a meaningful training session part-way through a flight as a passenger.
TOO