A320
Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Flight Crew Last 90 Days 152; Flight Crew Total 1503; Flight Crew Type 1229
Communication Breakdown; Confusion; Time Pressure
ATC Issue All Types; Conflict Airborne Conflict; Deviation - Altitude Overshoot; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural Clearance
Flight Crew Took Evasive Action
Procedure
We were climbing to 16;000 feet when we received an urgent radio call from Houston departure: '[Company] Traffic Alert; turn right to heading 330 immediately; maintain 11;000 feet.' During that radio call we also got an aural 'Traffic' alert from the TCAAS; with a target showing close off our left side 900 feet below us and climbing. I reached up; selected Heading mode and set 330 while the FO (First Officer) set 11;000 feet in the altitude window. I then disconnected the autopilot and increased the rate of turn. However; we were already at 11;600 feet and climbing when told to maintain 11;000 feet; with the traffic coming up from below; there was no way I was going to descend; so I maintained the climb while in the turn. We could hear other radio calls while maneuvering; but none with our call sign. As we passed 13;000 feet. Approach Control had us turn back left to a 310 heading; then a 260 heading. The FO asked Approach what altitude they wanted us at; and they responded '16;000 feet.' We set the altitude in the FCU; turned the autopilot back on; the flight continued normally. Our jumpseater; who was listening on his own earpiece; later stated that he heard approach telling someone to 'Expedite climb to 16;000 feet;' but didn't hear our call sign used. All of us agreed that either the call sign was blocked; or the Controller omitted it in the rush to avoid a mid-air collision. We never received a TCAS RA; just the 'Traffic' call; the Controller's immediate turn must have moved us out of the way before it deteriorated into an RA event. Closest altitude the FO saw was 600 feet below us; but not sure what the closest lateral separation was.
A320 Captain reported complying with aircraft indication instead of ATC instruction to avoid traffic.