A B747-F FLC CLBED ABOVE ASSIGNED ALT DEPARTING FROM ORD.

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DEPARTING ORD ON AUG/XA/99 APPROX XA45Z; ASSIGNED BY DEP CTL TO MAINTAIN 5000 FT AND HDG 090 DEGS. THE FO WAS THE PF. A SIGNIFICANT TSTM WAS IN OUR 9-11 O'CLOCK POS; MOVING L TO R. PRIOR TO TKOF; THE FO ADVISED TWR THAT WE WOULD REQUIRE A TURN SHORTLY AFTER TKOF ON RWY 9. THE TWR RPTED THEY DID NOT PAINT THE WX WE WERE CONCERNED ABOUT BUT REPLIED A TURN AFTER TKOF WOULD BE NO PROB. AFTER TKOF; DEP CTL ASSIGNED A L TURN TO 270 DEGS WHICH WOULD PUT US IN THE WX. THE CAPT TURNED DOWN THE CLRNC. DEP THEN ASSIGNED A R TURN TO 270 DEGS; WHICH WOULD HAVE BEEN OK AND WAS WHAT THE FO WAS EXPECTING. THE CAPT TURNED DOWN THAT CLRNC ALSO. DEP THEN ASKED WHAT HE WANTED TO DO; AND THE CAPT FURTHER COMPLICATED THINGS WITH A LENGTHY DISSERTATION NEITHER OF WHICH THE CTLR NOR THE FO UNDERSTOOD. AT THIS TIME WE WERE GOING THROUGH 5000 FT AND THE CTLR THEN SAID MAINTAIN 6000 FT; WHICH WE DID. THE CAPT WAS RELUCTANT TO TURN R; BUT A R TURN WAS MUCH BETTER THAN CONTINUING ON OUR PRESENT HDG BECAUSE WE WERE GETTING INTO THE BLOWOFF FROM THE STORM AT OUR 11:30 POS. BOTH PLTS WERE LOOKING AT THE RADAR WHEN THE ALT BUST OCCURRED. I THOUGHT WE HAD BEEN CLRED TO A HIGHER ALT BUT THE CAPT HAD TURNED DOWN THE CLRNC AND IN THE CONFUSION WE WENT THROUGH 5000 FT. CRM WAS NON EXISTENT AS THE CAPT WAS DICTATING TO EVERYONE WHAT TO DO AND WHEN TO DO IT. NOTHING WAS SAID BY DEP ABOUT GOING THROUGH 5000 FT. WE NEVER VERIFIED IF IT WAS AN ALT BUST OR NOT.