Small Transport; Low Wing; 2 Turbojet Eng
Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP)
Flight Crew Last 90 Days 180; Flight Crew Total 14000; Flight Crew Type 300
Distraction; Human-Machine Interface; Situational Awareness; Workload
Deviation - Altitude Overshoot; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter CFTT / CFIT
Flight Crew Became Reoriented; Flight Crew Overrode Automation
Software and Automation; Weather; Procedure; Airspace Structure; Human Factors
Center descended us to ZZZ in the hopes we would see the field; but the visibility was inadequate. We were then instructed to climb and received vectors for the GPS approach. The approach had been briefed and loaded into the FMS; but we weren't expecting to fly it.  Due to terrain; we were cleared for the approach from a high altitude requiring a steep descent to achieve the FAF altitude. We left center frequency and I began making position reports on CTAF.  I was heads up for most of it; and failed to realize the PF continued the high descent rate through the FAF altitude.  The altitude alerter was set to the approach minimums; and the flight director did command a level off; but the PM continued hand flying and disregarded the flight director.  I saw the ground throughout the entire approach; and felt we should have been close enough to see the runway and began to feel uneasy about how low we were with no runway in sight.  I looked at my PFD and realized the VPI was pegged full up.  I asked why we were so low; then I realized his mistake and directed him to level off.  We were about 800 AGL (5800 MSL); out side of the FAF which should have been crossed at 6800 MSL.  Then we saw the runway.  I called center back; cancelled IFR and we landed without further incident. Descending below a charted altitude on an approach is a big killer.  As a former sim instructor; check airman and ERC (Event Review Committee) ASAP rep; I've seen it happen several times to flight crews; and it almost always involves high workload and poor workload/automation management. I should have been a better PM by only taking occasional looks out the windshield; and backing him up inside. I shouldn't have set the approach mins in the altitude selector until level at the FAF altitude.  I am also new in type; and not as familiar with the automation as I needed to be.  The GPWS did verbalize a 'Caution Terrain'; but no 'Pull Up' command was received. What I feel worst about though is not commanding a missed approach; we had the gas for it.
Small transport Captain reported the pilot flying ignored the Flight Director command to level off and descended below the Final Approach Fix altitude prior to the fix resulting in a Ground Proximity alert.