GA flight instructor with student reported they were notified after the flight that they had flown below the MVA during an ILS approach.

Narrative

My student and I flew an instrument check ride preparation flight from MYF to ZZZ and back to fly three approaches. The flight was task saturated but otherwise uneventful. Upon landing; MYF ground informed us to call SoCal TRACON. After securing the aircraft; we called SoCal TRACON. After a couple back and fourth phone calls; TRACON informed us we flew below MVA on the ILS 28R into MYF. We were assigned an altitude of 3;800 feet; but I read back 3000 feet; and did not receive a correction from the controller. My student acknowledged 3;000 as well; and continued to descend. While diverting my attention briefly to look for traffic; we descended below 3;000 to 2;800 MSL. This caused us to go below minimum vectoring altitude; triggering an altitude alert from SoCal. The Controller quickly confirmed if we were established on the final approach course and he cleared us for the approach. This flight was conducted in daytime VMC conditions; and we had visual contact with all terrain and obstacles; as well as supplementary terrain/obstacle information on an L3 LYNX ADS-B receiver; ForeFlight on two iPads; and our Garmin G430W GPS. The primary cause of this communication breakdown between my student and myself was task saturation. I was focused on instructing and looking for traffic; and the student did not interpret the altitude assignment properly.Going forward; I will make sure my students and myself have a better understanding of the ATC clearances; and alleviate the task saturation when appropriate. I will also keep scanning inside the aircraft more frequently to check tolerances are being complied with.