I just tested doing a screenshot using the power and home buttons while talking to my wife on my 6s Plus. It worked fine. It also worked using Assistive Touch.
OP, Try again. Maybe your pressing one button too much ahead of the other.
Here's more about this:
Pressing the power button will, indeed, cut your conversation off of a call. But a screenshot by pressing both the power and home buttons should not end a call.
Note: If you're on speaker phone or a headset, the power button will not end the call.