A DEPARTING BE1900 OVERSHOOTS ITS INITIAL ASSIGNED ALT OF 4000 FT.

Narrative

THIS ALTDEV OCCURRED ON FLT FROM IAH TO TYR. AFTER DEPARTING IAH OFF OF RWY 15L; WE TURNED R TO A HDG OF 340 DEGS AND WERE RESTR TO AN ALT OF 4000 FT MSL. THIS DAY WAS A WX DAY IN TX AND I WAS THE PF OF THE ACFT. DURING THE CLB; I WAS OBSERVING A SUBSTANTIAL BUILDUP OF TWRING CUMULUS CLOUDS IN FRONT OF US. WHILE DOING THIS; I FAILED TO DETECT THAT I HAD CLBED THROUGH OUR ASSIGNED ALT OF 4000 FT. I DID NOT REALIZE THIS UNTIL 4400 FT IN THE CLB. WHILE ATTEMPTING TO LEVEL OFF; AND THEN TO DSND; THE DEP CTLR GAVE US AN AMENDED ALT OF 5000 FT MSL. MY FO WAS COMMUNICATING OUR OFF-TIMES TO OPS AND FAILED TO SEE THAT I FLEW THROUGH MY ALT RESTR. OUR ALT ALERTER WAS OPERATIONAL AND WE BOTH ACKNOWLEDGED AT 1000 FT TO GO UNTIL LEVELOFF. THIS OCCURRENCE HAPPENED DUE MY DISTR WITH THE WX INSTEAD OF MAINTAINING POSITIVE CTL OF THE ACFT WITH REGARDS TO ALT CTL. A BETTER SCAN AND POSSIBLY WAITING UNTIL WE WERE OUTSIDE OF THE CLASS B AIRSPACE TO CALL OPS WITH OUR OFF TIMES COULD HAVE PREVENTED THIS SIT. SUPPLEMENTAL INFO FROM ACN 429532: AT 3000 FT MSL; WE BOTH CALLED 1000 FT TO GO. AT ABOUT 3700 FT I TOLD THE CAPT THAT I WAS GOING TO CALL COMPANY. AS I HEARD THE ALT ALERTER GO OFF I LOOKED UP; ALT WAS 4300 FT MSL AND CLBING. I BROUGHT THIS TO THE ATTN OF THE CAPT. HE LEVELED OFF AT 4400 FT MSL; THEN ATC TOLD US TO CLB TO 5000 FT MSL. I WAS AT FAULT FOR CALLING COMPANY SOONER THAN I SHOULD HAVE.