AN A300-600 FLC OVERSHOT THEIR ASSIGNED ALT WHEN THE AUTOPLT ALT CAPTURE FAILED TO PERFORM AS EXPECTED. CREW WAS BUSY WITH OTHER TASKS.

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WE DEPARTED EWR RWY 22L; FO FLYING; ON A SID. DEP CTL GAVE US NUMEROUS HDG AND ALT CHANGES WHICH THE CAPT INPUT WHILE FO WAS HAND FLYING. AUTOPLT WAS TURNED ON THROUGH 10000 FT AND AT ABOUT THAT TIME WE WERE GIVEN A 250 KT SPD CTL. THE CAPT WAS ON THE RADIO WITH ATC AND PROGRAMMING THE FMS. JUST AFTER THAT WE WERE GIVEN A NEW HDG. I LOOKED UP AT THE FLT CTL PANEL TO DIAL IN THE NEW HDG AND AT THAT TIME THE ALT ALERT SOUNDED AT 11300 FT (WE WERE CLRED TO 11000 FT). BOTH PLTS IMMEDIATELY STARTED TO INITIATE THE DSCNT WITH THE CAPT ACTUALLY TURNING OFF THE AUTOPLT. THE AIRPLANE WAS LEVELED AT 11000 FT WITH NO KNOWN CONFLICTS. IN HINDSIGHT; I SHOULD HAVE ENGAGED THE AUTOPLT SOONER IN SUCH A HIGH WORKLOAD ENVIRONMENT. I BELIEVE WE WERE CLBING SO FAST THAT IT WAS HAVING PROBS CAPTURING. WITH THE CAPT LOOKING AT THE FMC AND ME LOOKING AT THE FCP AT JUST THE WRONG TIME; WE BOTH FAILED TO NOTICE THAT IT WASN'T CAPTURING. I BELIEVE THE MANY NEW INSTRUCTIONS FROM ATC DURING AN ALREADY VERY BUSY PERIOD ALSO CONTRIBUTED. SUPPLEMENTAL INFO FROM ACN 399391: APCHING 10000 FT WE WERE GIVEN A NEW HDG OF 360 DEGS AND AN AIRSPD RESTR OF 250 KIAS UNTIL FURTHER ADVISED. THE CAPT AT THAT POINT WENT HEADS DOWN TO INSERT THE 250 KT AIRSPD INTO THE FMS; WHILE ALSO NOTING AND VERIFYING 'PASSING 10000 FT FOR 11000 FT.' WE BOTH EXPECTED THE ACFT TO LEVEL OFF AT 11000 FT. WE QUICKLY DISCONNECTED THE AUTOPLT WITH THE ALTIMETER PEAKING OUT AT 11450 FT MSL. THEY DID SUBSEQUENTLY EXPLAIN; IN AN APOLOGETIC MANNER; FOR ALL THE VECTORING; ETC. AS A 2 PERSON CREW; I FELT WE WERE IN CTL OF THE ACFT AND SIT EXCEPT FOR THE EXPECTATION THAT THE AUTOPLT WOULD LEVEL THE ACFT. A MORE CLOSELY MONITORED LEVELOFF MAY HAVE PREVENTED THE DEV.