ALTDEV OCCURRED AS FLC'S ATTN WAS DIVERTED TO MANEUVERING TO AVOID TSTMS.

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CAPT WAS FLYING. WE WERE DEVIATING AROUND TSTMS. OUR CLRNC WAS TO CLB AND MAINTAIN 16000 FT. WE WERE BOTH LOOKING OUT THE WINDOWS FOR VISUAL DEVS AROUND TSTMS. AS WE CLBED; THE REQUIRED '2000 FT AND 1000 FT TO GO' CALLOUTS WERE MADE. AS WE APCHED 16000 FT MSL; I NOTICED WE WERE STILL CLBING (ON THE AUTOPLT) AT 2000 FPM. I ANNOUNCED 16000 FT AND THE CAPT MOVED THE AUTOPLT RATE KNOB TO MAINTAIN ALT. DURING THE AUTOPLT LEVELOFF; THE AIRPLANE 'OVERSHOT' BY ABOUT 250 FT. THE CAPT DISCONNECTED THE AUTOPLT AND STARTED A DSCNT TOWARD 16000 FT. WHEN I SAW THE CLB TREND REVERSE TOWARD 16000 FT; MY ATTN WENT TO SOMETHING ELSE. WHEN I LOOKED AT THE ALTIMETER AGAIN; WE WERE CLBING THROUGH 16300 FT AND MADE IT AS HIGH AS 16400 FT MSL. WE THEN WENT BACK TO 16000 FT MSL AND CONTINUED THE FLT. THE MAIN CONTRIBUTING FACTOR WAS OUR ATTN OUTSIDE THE ACFT (DEVIATING AROUND TSTMS). I PROBABLY SHOULD HAVE DIRECTED ALL OF MY ATTN TO THE ALT WHEN THE AUTOPLT WAS DISCONNECTED UNTIL WE MADE IT TO 16000 FT AND THE AUTOPLT WAS TURNED BACK ON.