Date: 201912
Local time of day: 0601-1200
Location: ZZZ.TRACON, US
Aircraft: B767 Undifferentiated or Other Model
Operator: Air Carrier
Operating under: Part 121
Mission: Passenger
Flight phase: Initial Approach
Airspace: Class B ZZZ
ATC / advisory: TRACON ZZZ
Reporter organization: Air Carrier
Reporter function: Captain; Pilot Flying
Second reporter function: Pilot Not Flying; Relief Pilot
Anomaly: ATC Issue All Types; Deviation - Altitude Excursion From Assigned Altitude; Deviation / Discrepancy - Procedural Clearance
Detector: Person Air Traffic Control
When detected: In-flight
Result: Flight Crew Returned To Clearance
Contributing factors: Procedure; Human Factors
Primary problem: Ambiguous

Narrative: At approximately 10 miles NW of ZZZ1 receiving vectors for final approach to ZZZ ILS RWY XXL; we were cleared to 5;000 feet. The First Officer; as the Pilot Monitoring; selected 5;000 in the altitude window and pointed at it. I; as the Pilot Flying; pointed at it and said '5;000'. I selected FLCH and the aircraft began descending to 5;000 from 6;000 [feet] Note; the Pilot Monitoring was using the radio call 'xxxx; Heavy'; while ATC was repeatedly using only our call sign without the qualifier 'Heavy'. Also note that there was a flight another company aircraft immediately in front of us getting vectored by same controller to the same runway. As such; just before the FMA annunciated Altitude Capture (ALT CAP) at 5000; ATC evidently cleared the company aircraft to descend to 3000 and cleared THAT AIRCRAFT for approach. Since ATC was not using the word 'Heavy' for us; and because of the similar sounding call signs so close together; the Pilot Monitoring selected 3000 in the altitude window and responded to the ATC clearance. I was not clear which call sign ATC said. I had noticed the Pilot Monitoring selected 3000 and was waiting for the response from ATC. I became fixated on listening for ATC; and then realized that under these conditions; being at 5000 and still about 10 miles from ZZZ1; it would be highly unusual for ATC to clear us to descend to 3000; and that we must have responded to the other aircraft's clearance. Now; since the Pilot Monitoring had selected a new altitude in the window before ALT CAP was annunciated in the FMA; and FLCH was engaged; and since the Pilot Flying was distracted and did not notice this; the aircraft descended below 5000; which was our actual clearance. By the time the Pilot Flying reacted and descent was arrested; ATC realized that we were descending erroneously and re-emphasized our clearance to only 5000. We noticed that we had descended to 4600 before descent was arrested and climb initiated back to 5;000 [feet]. Flight continued without incident to landing. No conflicts were noted.


Second narrative: I was the Relief Pilot sitting behind the [Pilot] Flying and Pilot Monitoring. We were about ten miles from ZZZ1; inbound to ZZZ for an ILS to XXL. The airport had just switched runways from [Runway] XYR to [Runway] XXL for arrivals and there was a lot of aircraft to be sequenced into the area. The frequency was very busy. VFR conditions allowed for tight spacing. Another company aircraft was ahead of us in line for approach. We were descending to 5;000 [feet] direct to ZZZ1 and the Pilot Monitoring answered a clearance to descend to 3;000 [feet] and cleared for the approach to [Runway] XXL. He dialed 3;000 [feet] in the altitude window and pointed at it; as is our procedure. I knew it was really early to be cleared for the approach and I knew there were aircraft in line ahead of us. As I began to speak out about my concern; I saw the Captain hesitate at the panel (altitude and approach mode) and he questioned the same things. We all realized it must have been for company aircraft and he only heard a portion in the congested frequency transmissions. By then the aircraft had reached 4;600 [feet]. The Captain (Pilot Flying) was already correcting. He corrected the altitude and they eventually were able to confirm we should still be at 5;000 [feet] with Approach. The rest of the approach continued uneventfully.


Synopsis: B-767 flight crew reported complying with an ATC descent clearance intended for a company aircraft.