A wide body flight crew suffered a track deviation when all three pilots misunderstood an approach clearance.

Narrative

Approaching XXX. Received clearance to turn to 020 and intercept the localizer for Runway XXL. I did not hear the full clearance. The pilot not flying read back; turn to 020 and intercept the localizer for XXL. There was a fleet qualified pilot in the observer seat and on a headset. About 2 miles after turning to 020; approach asked if we turned prior to XXX? We answered in the affirmative. They then turned us to 050 to avoid restricted airspace. Abeam XXX they cleared us to XXXXX and to intercept the localizer for XXL. Based on the correction by ATC; I assumed the original clearance was turn to 020 after XXX and intercept the XXL localizer. There didn't appear to be any other aircraft around us at the time. I should have received confirmation of the clearance from ATC. Contributing factor was the headsets available on the airplane. It appears the company is replacing the single earpiece boom microphones with dual earpiece headsets; similar to what is used in the simulator. The headsets make communications with ATC and other crewmembers difficult.