ALTDEV ALT OVERSHOT IN CLB.

Narrative

WHILE ON DEP FROM SAT WE WERE CLRED TO 8000 FT. I WAS FLYING THE DEP AS THE FO; AND WAS HAVING TO DEVIATE EXTENSIVELY IN THE CLBOUT FOR SEVERAL TSTMS THAT WERE IN AND AROUND THE DEP CLB. I ENGAGED THE AUTOPLT TO FREE UP MY ATTN FOR THE WX AVOIDANCE. I ENGAGED THE SPD SELECT MODE FOR THE PWR SETTING; AND THE VERT SPD MODE FOR THE CLB. 8000 FT WAS SET AND INDICATED ARMED IN THE FLT GUIDANCE SYS DISPLAY AND THE VERT SPD WAS AT APPROX 1600 FPM. WE HAD JUST BEEN GIVEN A HDG BY DEP CTL AND WERE IN THE PROCESS OF CLRING A COUPLE OF TSTM CELLS WHEN THE ALT ALERT HORN WENT OFF. WE WERE PASSING THROUGH 8300 FT AND I IMMEDIATELY DISCONNECTED THE AUTOPLT AND AUTOTHROTTLES AND LOWERED THE NOSE TO BRING THE ACFT BACK DOWN TO 8000 FT. JUST PRIOR TO LEVELING AT 8000 FT; THE DEP CTLR GAVE US A CLB CLRNC TO 13000 FT. THE CTLR MADE NO MENTION OF OUR INADVERTENT ALTDEV; PRIOR TO HANDING US OFF TO ZHU. DEP CTL FREQ WAS 125.1 AND WE WERE APPROX 10-20 NM FROM THE SAT VOR. THE HIGHEST ALT IN THE DEV WAS APPROX 8500 FT. THE TIME THAT WE NEEDED THE AUTOMATION THE MOST WAS TIME THAT WE NEEDED TO BE THE MOST VIGILANT OF THE TOTAL PICTURE.