ASRS 2000682

While practicing landings on Runway XXL at ZZZ airport, a helicopter was practicing touch and goes using a left pattern for Runway XXR. Over the CTAF, a miscommunication occured regarding the timing of a takeoff. My student and I believed the helicopter was making a full stop on the runway based on their radio call, and indicated we would wait for their landing before departing. After they appeared to stop, we made a departure call and began a takeoff roll. The helicopter then began proceeding upwind. By then, I was unsure we would be able to safely abort the takeoff, so I continued upwind, keeping the helicopter in sight. I attempted to contact the helicopter on the CTAF about their intentions, and twice received no reply. They then announced a left crosswind departure. I leveled off, anticipating they would continue their climb and turn above me, announced my position, and asked if they had me in sight. They looked and seemed to visually acquire me at this time. I am unsure whether separation actually fell below 500 feet, but I figured the potentially hazardous situation caused by lack of communication at a hazardous airport was worth the report. I was later informed that helicopters do not always touch down and "taxi back" ZZZ based on operating restrictions, and believe my own lack of familiarity with helicopter pattern operations may have been a factor as well.