Date: 202106
Local time of day: 1201-1800
Location: ZZZ.Airport, US
Flight conditions: IMC
Weather elements / visibility: 10
Light: Daylight
Aircraft: Helicopter
Operator: Military
Operating under: Part 91
Flight plan: SVFR
Mission: Training
Flight phase: Takeoff / Launch
Airspace: Class C ZZZ
ATC / advisory: Tower ZZZ
Second aircraft: Small Transport; Low Wing; 2 Turbojet Eng
Reporter organization: Military
Reporter function: Captain; Instructor; Pilot Not Flying
Reporter qualification: Flight Crew Commercial; Flight Crew Flight Instructor; Flight Crew Instrument
Human factors: Communication Breakdown; Situational Awareness
Anomaly: Conflict NMAC; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural Clearance
Detector: Person Air Traffic Control
When detected: In-flight
Result: General None Reported / Taken
Contributing factors: Procedure; Staffing; Human Factors
Primary problem: Human Factors

Narrative: Flight started at the helicopter pads - second flight out of ZZZ for the day. This was a training flight with students. I was the Flight Instructor. I started up and prepared for takeoff as normal. The weather was IFR which required a SVFR clearance for our departure. I received weather and contacted Ground and requested the SVFR to the northeast with a present position departure from the helicopter pads. This was the expected as we had done so earlier. Initially; I was told to standby while the Controller was getting other aircraft taxiing. After the wait; the Controller came back and cleared us to the northeast at or below 1700 ft. via SVFR; which I read back. Despite still being on Ground frequency; I erroneously mistook the SVFR clearance as a clearance to takeoff as requested from present position. As such; I instructed the student to initiate the takeoff and depart; which we did.Our flight path was to the northeast which took us across Runway X; the active. As we reached 500 ft. and [was] approaching clear of the ZZZ Class 'C;' I expected a switch to Approach as usual but when I looked down at the radio I saw we were still on the Ground frequency. I quickly switched to Tower and was informed of my lack of takeoff clearance and additionally the overflight of an aircraft on takeoff from Runway X which we didn't see. Our departure flight path was at a 40-degree offset roughly 040; which put the start of Runway 8 behind us. Sitting on the right side; I didn't see Aircraft Y who was actually cleared for takeoff start their roll at roughly the same time as we did. Due to the angle; they were aft of my scan during the takeoff. Based on the info from the Controller; we passed over them by about 200 ft. as they were departing. Because we were still on the Ground frequency; we also didn't hear towers call to us when we started to depart without takeoff clearance. Unfortunately; all of this was caused by my assumption of having received a takeoff clearance and acting accordingly. Obviously; I should have been more aware and realized that it wasn't a takeoff clearance that was issued. I should have also noticed that we had not switched to Tower from Ground earlier. Not to pass blame; but an observation - it is common for a Ground Controller after issuing a clearance to push us to the next Controller; i.e.; 'Read back correct; contact Tower/Ground for takeoff/taxi.' This would seem more critical; particularly for a helicopter present position departure such as this one that does not require a taxi to a specific runway. In this case; that was not stated as far as I can remember. Additionally; there has been a lot of Ground and Tower combined frequencies lately and that also could have played into the confirmation bias that led to assuming my SVFR clearance was also a takeoff clearance and not switching to the Tower frequency. In this case; Tower and Ground were on different frequencies. Regardless; I have executed present position departures many times and not had an issue like this and I definitely made a mistake which almost resulted in a collision. In the future; I will exercise extreme caution and slow down to ensure this mistake does not happen again.




Synopsis: Flight Instructor reported mistakenly taking off without clearance which led to an NMAC event with another aircraft taking off.