C172 Flight Instructor reported entering an unusual attitude and momentary loss of control twice during a training flight. Instructor regained control of aircraft after events.

Narrative

At approximately XA20am local time I was conducting a training flight with a student. While demoing the concept of the variable back pressure being used based on bank angle; I increased the bank angle in a right turn. I referenced the attitude indicator as I increased the bank angle to 55 degrees (showing the aerodynamics in play in a steep turn). While demoing this; I inadvertently went past 60 degrees of bank when the attitude indicator was out of my field of view. Upon realizing that this occurred; I promptly reduced back pressure and decreased the bank angle below the 60 degree limit.Deciding that the altitude we were flying at was unsuitable for the current visibility; I elected to conduct a descent via a spiral; down to a lower altitude. During the descent; the cloud bases and haze caused a second momentary departure to a steeper bank attitude than I intended and again exceeded 60 degrees. I believe this occurred because of the hazy flight condition and slanted clouds. This condition ultimately presented a false horizon out the windshield. The false horizon was apparent only when referencing the flight instruments. This was the first time that I have ever seen such a convincing false horizon in my flying. The entire occurrence has given me a fresh respect for how easy an unusual attitude can occur.