You can for sure fit three 20 minute hiit sessions. If you’re lifting mon-wed-fri throw them in tuesday thursday saturday.At first the muscles used in the hiit are going to perform worse than usual on lifting days. This doesn’t necessarily mean you are actually getting weaker (losing contractile protein[muscle])…. Sometimes performance can suffer because you are exercising without 100% recovery, and this is ok, it doesn’t necessarily mean you lost muscle, you may just be partially glycogen depleted… (and this issue, with reduced performance, will decrease with time, as your body adapts to the hiit)…
I have extensive knowledge of these types of routines and used to work in a gym that offered nothing but group fitness classes in hiit style training.
If you need any help with creativity, finding movements, running speeds, and appropriate intensities, email me @ email@example.com
Sometimes the intensity that is significantly harder than cardio yet significantly less intense than strength training is hard to nail down (exercise selection [and resistance] wise). You can do it on a rower, you can do it on stairs or a stairclimber, you can do it on a treadmill, or you can do it the way you were proposing, with bodyweight mixed with typical interval stuff.
I have actual equations you can use based on maxes and sprint times to calculate exactly what speed/weight will create proper failure in the right interval (time wise). (for you, you want absolute failure to occur at 20 minutes[end of workout]… and you want to repeatedly come VERY close to failure at the end of the intervals leading up to that last one).
The key here is that time is the factor being measured, both recovery and exertion time, NOT speed or weight lifted. Terms such as FAILURE are irrelevant. In typical hiit you truly fail once (per workout), and that is the last interval of the workout (assuming the workout is contructed properly). Every other interval you should be coming progressively closer to failure, until the final one where you actually fail.