FLC OF AN MLG OVERSHOT ALT ON DSCNT.

Narrative

WHILE AT CRUISE INBOUND TO BHM; WE RECEIVED CLRNC TO CROSS 30 MI SE OF BHM AT 11000 FT FROM ZTL. AT THIS TIME I DID MY PA; WHICH UPON COMPLETION THE FO INDICATED THAT ZTL WANTED US TO START DOWN NOW FOR 13000 FT. I MISINTERPRETED THIS TO MEAN WE NEEDED TO DSND THROUGH 13000 FT FOR TFC. PASSING THROUGH APPROX 13000 FT; I VISUALLY ACQUIRED OUR TFC AND SAW IT ON TCASII; IT WAS AT 12000 FT VICE THE 14000 FT I WAS EXPECTING. AT THIS POINT WE WERE IN A HIGH RATE OF DSCNT AND I REALIZED I WOULD PROVIDE MORE SEPARATION IF I EXPEDITED DOWN TO 11000 FT VICE TRYING TO PULL UP AND BOTTOM OUT AT AN ALT CLOSE TO 12000 FT. I CALLED ZTL LATER AND THE SUPVR SAID OUR CLOSEST SEPARATION WAS 3.46 MI BUT THAT THEY WERE FILING A PLT ERROR RPT SINCE THE FO HAD READ BACK 13000 FT ON THE TAPE. THE FO TOLD ME THAT THE PHRASEOLOGY USED BY THE CTLR LED HIM TO BELIEVE THAT THE INITIAL CLRNC OF 11000 FT AT 30 MI STILL APPLIED; AND THEREFORE DID NOT SET 13000 FT IN THE ALT WINDOW. TO MY KNOWLEDGE NEITHER ACFT TOOK EVASIVE ACTION.