Light transport flight crew reported low altitude alert by ATC during descent into SAN.

Narrative

PF was hand flying aircraft. PNF was managing communications and FMS programming. Aircraft was cleared to descend to 9000 and direct to NESTY. Aircraft descended below the assigned altitude. Upon noticing descent below assigned altitude (~100ft); PNF stated 'altitude'. PF did not respond. PNF was determining vRef and verifying approach procedure and did not verify the PF had initiated climb to assigned altitude for several seconds. PNF stated 'climb'. PF did not acknowledge or initiate climb. ATC issued a low altitude alert. PNF stated 'my controls'. PF acknowledged. PNF took control of the aircraft and initiated climb to assigned altitude. Flight continued without further incident.I believe the incident occurred because the PNF was distracted by other tasks and was not adequately monitoring the aircraft during the descent. The PF said that he was monitoring ATIS at the destination airport and did not hear the PNF or recognize the descent below the assigned altitude. Clearly the PF was also distracted. The incident was the result of both pilots being distracted during the descent and not adequately monitoring altitude. Other contributing factors may include the PF's lack of experience in the aircraft and the PIC's advice to the SIC (PF) that a common crossing altitude at NEST was be 3800 feet and to ensure that the rate of descent would be sufficient to meet that. The PIC and SIC had limited experience working as a crew. Had the PIC's/PNF attention been appropriately focused I do not believe the incident would have occurred. The PF had limited experience operating the aircraft and; given that; the PIC's primary focus during the descent should have been monitoring the aircraft.