GIV Captain reports descending below 10000 feet at KRAIN on the ILS 25L at LAX. Neither pilot is able to quickly ascertain the correct altitude at KRAIN from their government approach charts.

Narrative

We were flying the RIIVR Arrival to the ILS 25L LAX. Upon loading the arrival and approach expected; we found a duplicate point in the FMS (GRAMM). After discussion; we decided to leave the duplicate point. Passing FL250; we were cleared to descend via the RIIVR Arrival. We placed 12000 MSL in the altitude select window. VNAV; LNAV; and the autopilot were all engaged during the descent. Passing GRAMM; the LNAV disengaged with an amber caution (CPL data invalid) that our FMS had flown past the final FMS point. The pilot not flying (PNF) fixed the FMS issues; and we reengaged the VNAV and LNAV. The vertical descent was not performing smoothly at this point; so I disengaged the autopilot. We leveled at 12000 MSL at RIIVR and we were cleared for the ILS 25L. With VNAV guidance provided on the PFD screen and still hand flying the aircraft; we placed the altitude select at 5000 MSL for point GAATE on the approach. In hind sight; we should have stepped the altitude down at each fix. Passing 110000 MSL we were given an airspeed of 230 knots. Just prior to LUVYN; I asked the PNF what the next altitude restriction was. The PNF stated 9000 MSL. Just past 10000 MSL; the PFD VNAV altitude of 10000 MSL turned amber. At this point I added power and slowed the descent. I asked the PNF again for the altitude required at KRAIN and he repeated 9000 MSL. With a small descent rate; I glanced to the DOD approach chart and was unable to quickly locate position or altitude. I added more power for a level off and then SOCAL called us to inform us that we were a few hundred feet below the required 10000 MSL at KRAIN. I climbed from 9700 MSL to 10000 MSL and then continued the approach. PNF stated he read the incorrect side of the fix for the altitude after the notification of the deviation. I shouldn't have continued below 10000 until verifying the altitude myself.