Flight Instructor with student reported a NMAC with a helicopter during takeoff from a non-towered airport.

Narrative

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.