AN LR35 CHARTER FLT OVERSHOOTS ITS AMENDED ALT IN CLBOUT OF BUR; CA.

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BEFORE TAXIING TO THE TKOF RWY; WE PICKED UP OUR IFR CLRNC. THE INITIAL ALT WE RECEIVED WAS 13000 FT. THE COPLT WAS THE PF FOR OUR TRIP FROM BUR TO LAS. I WAS IN THE R SEAT AND HANDLING THE RADIO COMS. PART OF OUR TKOF CLRNC WAS AN INSTRUCTION TO CLB AND MAINTAIN 5000 FT (INSTEAD OF THE 13000 FT WHICH WE HAD BRIEFED IN OUR BEFORE TKOF CREW BRIEFING.) I SET 5000 FT IN THE ALT ALERTER AND POINTED OUT THE REVISED INITIAL ALT TO THE PF. AFTER TKOF; WE PERFORMED A NOISE ABATEMENT DEP. AT 4000 FT THE ALT ALERTER CHIMED THE '1000 FT TO GO' WARNING. I POINTED OUT THE ALT TO THE PF; BUT DIDN'T MONITOR HER ACTIONS TO SEE IF SHE INITIATED THE LEVELOFF. NEITHER OF US REALIZED THAT WE HAD PASSED THROUGH OUR ASSIGNED ALT UNTIL WE WERE AT 5400 FT. CORRECTIVE ACTION WAS TAKEN AND THE TREND REVERSED. I CONTACTED ATC (SOCAL APCH) AND INFORMED THEM OF THE TRANSGRESSION AND ASKED IF WE COULD CONTINUE TO CLB. THEY RESPONDED IN THE NEGATIVE. BY THIS TIME WE WERE ONCE AGAIN AT 5000 FT. I INFORMED ATC THAT WE WERE AT 5000 FT MSL. THE REST OF THE FLT WAS UNEVENTFUL. THE TRANSGRESSION HAPPENED PARTLY BECAUSE OF THE HIGH WORKLOAD ON THE CREW CAUSED BY THE CONDITIONS (RAIN; ICING CONDITIONS; TURB) AND PRESENCE OF LOW LEVEL TSTMS WHICH WE WERE INTENT ON AVOIDING. PLUS THE NEED TO DO A NOISE ABATEMENT DEP; AND PARTLY BECAUSE I HADN'T CONFIRMED THAT THE PF FULLY UNDERSTOOD THE REVISED INITIAL ALT GIVEN JUST PRIOR TO TAKING OFF; SHE HADN'T; AND WAS CHEERFULLY HDG FOR 13000 FT MSL AND HAD MISSED MY '1000 FT TO GO' CALL AT 4000 FT. I SHOULD HAVE MONITORED HER ACTIONS MORE CLOSELY AND CHKED TO SEE THAT SHE WAS LEVELING OFF.