B737 Undifferentiated or Other Model
Flight Crew Air Transport Pilot (ATP)
Flight Crew Last 90 Days 161; Flight Crew Type 9500
Communication Breakdown; Situational Awareness
ATC Issue All Types; Deviation - Altitude Excursion From Assigned Altitude; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter CFTT / CFIT
Air Traffic Control Issued Advisory / Alert; Flight Crew Became Reoriented
Human Factors
We were cleared to intercept the Localizer for RWY 12R at SAT at about 12 DME. Both the First Officer and I both heard ATC state maintain at or above 2000 feet until established and cleared the ILS 12R. We were also looking for the airport as we were being vectored onto the approach; (and descending through 2500 feet) when ATC told us she had an altitude alert and we needed to maintain at or above 2800 feet; until established on the approach. I immediately disconnected the autopilot and climbed back to 2800 feet MSL.  We intercepted the localizer and glideslope and the remainder of the approach and landing was uneventful. Preventative Measures: I should have paid more attention to the approach chart altitude; and queried the Controller when what we heard did not match with the approach chart. ATC was speaking quite fast; so if they slowed down a little; maybe we would have heard the correct altitude.
B737 Captain reported descending below charted altitude on approach to SAT when the flight crew misunderstood ATC clearance.