Cessna 172 Flight Instructor trainee reported a loss of controlled flight and aircraft flight control upset when receiving stall and spin training from another flight instructor. The trainee indicated a loss of situational awareness by the instructor before recovering the aircraft and returning for a landing.

Narrative

Was receiving spin training from my instructor(CFI/CFII/MEI) in a Cessna 172; required for my CFI training. Although I have time in the 172; I have not flown the aircraft type in several years. All my cert/rating training since PPL has occurred in the PA28.My instructor was PIC; as I have no aerobatic training -- and had no spin training prior tothis flight.We had extra time at the end of our launch time after I received all required spin training; so my instructor chose to demonstrate various demonstration stalls that are traditionally incipient-stall only to a full stall; to demonstrate what can happen (a spin).While my instructor was attempting to demonstrate an accelerated-stall to a full stall; the stall didn't break and my instructor let the aircraft continue banking into a spiral-dive type maneuver. This gained quite a bit of airspeed -- I cannot recall the exact value since I was simply observing the maneuvering. It was somewhere in the rough ballpark of 120; from the best of my knowledge. To bleed off this airspeed; my instructor proceeded to pitch the aircraft up quite aggressively. He let the pitch attitude rise past 30 degrees; past 60 degrees; and eventually all the way to 80-90 degrees pitch up. Having never experienced an unusual attitude this extreme before; and because I falsely assumed my instructor knew what he was doing; I did not take control or attempt to recover. I partially blame this to me being far out of my element; combined with the shock of such an abrupt and unscripted maneuver.My instructor later noted that he'd done this before and the airspeed gained from the botched accelerated stall has always bled off before exceeding any limitations; so I theorize that he fixated on the airspeed and just kept pitching up to bleed it off as he'd done before; not noticing the rapidly increasing pitch attitude.Our airspeed quickly bled below a displayable number on our G1000 PFD; and my instructor momentarily lost control authority of the aircraft. We later noted that we most likely experienced a stall across all flight surfaces; including the tailplane; as our airspeed reached approximately zero. The details at this point are somewhat vague; but I will describe to the best of my ability. At this point I knew my instructor had lost control; as there were plenty of expletives coming from him. He pushes forward on the yoke and nothing occurs; we are just hanging in a vertical attitude with exceptionally low airspeed. I assume at this point he realizes there's been an tailplane stall; and applies back pressure to recover. The nose slowly drops down and eventually weathervanes downward towards the ground at very steep angle; around 90 degrees pitch down now. The negative G's from this reversal causes my instructor's door latch to open slightly -- not a fully open door; but roughly a half-inch crack. All the unsecured items on my instructor's kneeboard become airborne; such as his checklist. The aircraft eventually gains enough airspeed for solid control effectiveness; and my instructor pulls out of the dive while in the yellow airspeed arc.After getting over the initial shock of what just happened; I hand my instructor's checklist back (which landed on me during the recovery) and notice his door is open. My instructor proceeds to re-latch his door; and to my surprise; continues to demonstrate more maneuvers despite that upset. I was quite scared at this point and wasn't sure what to say to this. In hindsight; I certainly wish I had taken controls as soon as the aircraft exceeded pitch attitude limits; and also insisted we return to the airport immediately thereafter. I was in shock at the maneuver and falsely believed my instructor was in control until it was too late.A few minutes later; we return back to the ZZZ airport without further upset. My instructor stated the aircraft flew fine thereafter; as I did not touch the controls throughout any of this. My instructor later wrote up a maintenance discrepancy report for possible G exceedance; and I promptly filed a report about the incident to my school's safetyreporting system.