FLC ON A CL601 DEPARTED BHM IFR AND WERE CLRED TO CRUISE AT 4000 FT. THE FO; FLYING FROM THE L SEAT; INADVERTENTLY OVERSHOT THE ALT TO 4500 FT. THE ERROR WAS IMMEDIATELY NOTICED BY THE CREW AND DSCNT WAS MADE BACK TO 4000 FT. NO OTHER ACFT WAS INVOLVED.

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MY FO WAS FLYING THE CHALLENGER FROM THE L SEAT. AFTER TAKING OFF FROM THE BHM ARPT WE WERE CLRED TO CRUISE AT 4000 FT. THERE WERE TSTMS IN THE AREA AND ALONG OUR RTE TO MONTGOMERY; AL. I WAS INVOLVED IN THE AFTER TKOF CHKLIST AND THE WX RADAR TO AVOID THE WX. I INADVERTENTLY MISSED THE ALT CHK AT 4000 FT. MY FO CALLED MY ATTN TO THE ALTIMETER GOING THROUGH 4400 FT AND I QUICKLY TOLD HIM TO DSND BACK TO 4000 FT. DURING THE ROUND OVER THE ACFT PEAKED THE ALT AT 4500 FT THEN DSNDED BACK TO 4000 FT. THE ACFT WAS OFF ALT APPROX 20 SECONDS. THE BHM APCH CTLR DID NOT SAY ANYTHING ABOUT THE ALT VIOLATION AND I DID NOT SEE ANY ACFT WITHIN OUR TCASII 10 MI RANGE. ALT VIOLATIONS ARE ALWAYS A POTENTIAL THREAT TO AVIATION AND CONSTANT ALT MONITORING IS VERY IMPORTANT. THE PF SHOULD ALWAYS CALL OUT THE ALT 1000 FT BELOW OR ABOVE THE ASSIGNED ALT DURING THE ASCENDING OR DSNDING OF THE ACFT. THE PNF SHOULD THEN CHK THE ALT AND GIVE VERBAL CONFIRMATION. WX CAN BE A THREAT TO AVIATION SAFETY AND CHKLIST DUTIES CAN BE DISTRACTING. HOWEVER; PLTS SHOULD NEVER DIVERT ATTN AWAY FROM THE BASICS OF SAFE FLT.