BD700 pilot reported receiving a low altitude alert from ATC due to descent below assigned altitude. Flight crew climbed back to assigned altitude.

Narrative

The flight consisted of two contract pilots who had never flown together and into a mountainous terrain airport-ZZZ. The NFP's (Non-flying Pilot) first (primary) language was NOT English.Numerous times the FP (Flying Pilot) would take over the radios due to the NFP's accent or missed radio calls due to the call sign. The crew was in the hold at ZZZ [VOR]; configuring for an approach into ZZZ. The current winds exceeded the tailwind component of the aircraft. There was also an airplane below holding. Passengers were interrupting the crew regarding the delay and a possible diversion. The weather pasted the airport and the winds changed 180 degrees allowing an acceptable approach.The preceeding aircraft below completed the approach and gave a PIREP and the controller relayed the PIREP and new winds and weather. The NFP entered the new information in the FMS. The captain elected for a descent and box vectors to reduce the high workload.ATC issued a descent to XX000. The crew believes they responded XX;000. However XY;000 was put in the altitude selector. The crew descended to XY;300 feet when ATC issued an altitude warning and the FP initiated an immediate climb to XX;000. The MSA in the area is XY700 feet.The crew regained altitude and intercepted the approach course; followed by a successful landing.Situation: High workload; Mountainous terrain; High altitude airport; Bad weather; Passenger interference during a critical stage of flight. Two contractors who have never flown together.Lessons learned: Do not let the passengers interrupt during critical phases of flight. Check/double check altitude clearances-if in doubt-verify/along with cross referencing MSA posted altitude.