MIL PLT OVERSHOOTS ASSIGNED ALT ON CLB.

Narrative

JUST PRIOR TO TAKE OFF FROM NAS NEW ORLEANS; THE COPLT RECEIVED AN INITIAL CLB ALT CHANGE FROM 13000-6000 FT ON DEP. I WAS DOING A CHKLIST ITEM AND DO NOT REMEMBER RECEIVING THE CHANGE. JUST AFTER TKOF ON RWY 04 WE WERE GIVEN A VECTOR BY NEW ORLEANS DEP TO THE E TO AVOID WX. (TSTMS). THE COPLT WAS BUSY DOING A CHKLIST WHILE I ATTEMPTED TO AVOID THE SEVERE WX BY USE OF THE WX RADAR. I BECAME PREOCCUPIED WITH WX AVOIDANCE AND MISSED THE ALT ALERT. THERE WAS A LOT OF RADIO CHATTER AT THE TIME. WHEN WE GOT TO ABOUT 7600 FT DEP CALLED AND ASKED OUR ALT; THAT'S WHEN I NOTICED 6000 FT SET IN THE ALT ALERT. I IMMEDIATELY INITIATED A DSCNT TOWARDS 6000 FT. AT APPROX 6500 FT I WAS GIVEN A CLB TO 13000 FT. I BELIEVE THERE WERE A COUPLE OF CAUSES TO THIS INCIDENT. BETTER CREW/COCKPIT COORD ON THE GND AND IN THE AIR WOULD HAVE CORRECTED THE PROB. WHEN I FELT THAT I WAS BECOMING OVERLOADED I SHOULD HAVE TOLD THE COPLT TO STOP THE CHKLIST AND CONCENTRATE ON HELPING ME WITH THE RADIOS AND THE WX RADAR. THE COPLT IS NEW TO THE AIRPLANE AND I HAD NOT FLOWN IN ABOUT 21 DAYS SO MY CURRENCY WAS NOT AS GOOD AS IT COULD HAVE BEEN. I LET MYSELF GET OVERLOADED. THE BEST WAY TO OVERCOME THIS PROB IS TO STRESS BETTER CREW COORD AND TO CONFIRM ASSIGNED ALTS WITH EACH OTHER VERBALLY WHEN NEW ONES ARE ASSIGNED.