MLG ACFT ON ARR ROUTING AND ALT RESTR DEVIATED AROUND WX AND DSNDED 500 FT BELOW ASSIGNED ALT.

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DURING DSCNT ON THE OLYMPIA 2 ARR TO SEATTLE; EXPERIENCED COPLT WAS HAND FLYING THE ACFT; WHICH IS COMMON TO MAINTAIN PROFICIENCY. WE HAD RECEIVED CLRNC TO 'DSND VIA THE OLYMPIA 2 ARR LNDG S' WHICH MEANT WE WERE GOOD TO DSND TO 16000 FT OVER OLYMPIA VOR AND THEN DOWN TO 12000 FT. AS WE APCHED OLM VOR IT WAS CLR WE WOULD HAVE TO DEV AROUND A CLOUD BUILDUP. AT THIS TIME; I BELIEVE WE WERE TALKING TO SEA APCH CTL. THE CTLR TOLD US TO DEV TO THE W OF THE BUILDUP AND TO MAINTAIN 13000 FT. WE CONTINUED TO DSND BELOW 16000 FT AS WE DEVIATED AROUND THE BUILDUP. AS WE CLRED THE BUILDUP; I TOLD THE CTLR THAT WE COULD TURN BACK ON COURSE. THE CTLR CLRED US BACK ON COURSE AND ABOUT THIS TIME ASKED US OUR ALT WHICH WAS ABOUT 12500 FT. WHEN I RPTED '12500 FT CORRECTING;' THE CTLR CLRED US TO CONTINUE DSCNT TO 12000 FT. THE REMAINDER OF THE APCH AND LNDG WAS UNEVENTFUL. MY ONLY SUGGESTION FOR PRECLUDING A SIMILAR MISTAKE IS TO ENCOURAGE USE OF THE AUTOPLT DURING HIGH WORKLOAD OR ABNORMAL EVENTS DURING FLT; SUCH AS OUR DEV AROUND WX DURING DSCNT. THE AUTOPLT AND MCP WERE PROPERLY SET UP INCLUDING THE ALT ALERTER; BUT BECAUSE THE AIRPLANE WAS BEING HAND FLOWN; AND WORKLOAD WAS RELATIVELY HIGH WITH APCH CTL RADIO XMISSIONS AND DEV AROUND WX; NEITHER ME NOR THE COPLT HEARD THE ALT ALERTER CHIMES TELLING US WE HAD FLOWN BELOW OUR ASSIGNED ALT OF 13000 FT.