Light Transport; Low Wing; 2 Turbojet Eng
Flight Crew Instrument; Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP); Flight Crew Flight Instructor
Flight Crew Last 90 Days 120; Flight Crew Total 8400; Flight Crew Type 1200
Situational Awareness; Time Pressure; Workload; Confusion; Communication Breakdown
ATC Issue All Types; Conflict NMAC; Deviation - Altitude Overshoot; Deviation - Altitude Crossing Restriction Not Met; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Issued Advisory / Alert; Flight Crew Took Evasive Action
Human Factors
Talking to ZZZ Center. Was assigned; what we thought; was an altitude of FL370. We read back FL370. ATC specialist actually assigned us FL270; but didn't correct our read back. A few minutes after the altitude assignment; ATC then advised us of crossing traffic at FL280.Upon us passing FL275 MSL; ATC queried if we were level at FL270. We advised ATC that we were climbing to our assigned altitude of FL370.ATC then clarified our clearance of FL270. Autopilot was disconnected and a return to FL270 was commenced as the other aircraft was given a heading assignment to further relieve the conflict.At no point did we receive a TA or RA; nor did the conflicting traffic report either.
[Narrative contained no additional information.]
Air taxi flight crew reported climbing through their assigned altitude. On read-back to ATC the pilots were not corrected that their stated altitude was incorrect. There was no RA.