Commercial Fixed Wing
Flight Crew Air Transport Pilot (ATP)
Distraction
Deviation - Altitude Excursion From Assigned Altitude; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Issued Advisory / Alert; Flight Crew Returned To Clearance
Human Factors
While in cruise; I was able to pick up the visual on the MKK airport. The First Officer called HCF and told them we have the airport in sight. I remember the controller asking if we had the preceding King Air 12 miles in front of us in sight. We did not have the aircraft in sight; but I thought at the time that we had been cleared for the visual anyways. I even confirmed it with the First Officer because the instructions were not very clear. I started a descent and a turn to the left about 20 degrees to approach the airport from the north. Upon reaching 4;300 ft MSL; the controller asked what our assigned altitude was. He informed us that we had not been cleared for the visual approach and to climb back to 5;000 ft MSL. He then vectored us to the MKK VOR; at which time we were able to see the King Air nearing the airport. We called the aircraft in sight; at which time we were cleared for the visual into MKK. The First Officer and I discussed the situation and concluded that the controller's instructions were not clear; leading to our confusion on whether or not we were cleared for the visual approach. Another factor that may have lead to this mistake was that I was spending most of my time during the flight explaining the airspace and aircraft features to the new First Officer. This distraction may have played a roll in my misunderstanding of our clearance.
Air carrier Captain reported they descended before being cleared by ATC for a visual approach to MKK.