FLC OF A BEECH 200 TURBOPROP OVERSHOT ASSIGNED ALT DURING CLB DUE TO MISUNDERSTANDING THE CLRNC ALT.

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WE WERE CLRED FOR TKOF AND AFTER CONTACTING FAY; PNF LOOKED IN AN ENRTE CHART; PNF RPTED WE WERE OUT OF 1500 FT FOR 5000 FT; TURNING TO 270 DEGS. FAY CAME BACK WITH CLB AND MAINTAIN 4000 FT NOW AND HDG 280 DEGS. PNF SAID WE WOULD STOP THE CLB AT 4000 FT. SHORTLY; HE SAID TO TURN R TO 240 DEGS AND CLB AND MAINTAIN 10000 FT. PNF SAID IN AN INQUISITIVE VOICE; 'R TURN TO 240 DEGS?' AND HE SAID 'NEGATIVE; R TURN TO 340 DEGS AND CLB AND MAINTAIN 10000 FT' AND PNF SAID 'R TURN TO 340 DEGS CLB AND MAINTAIN 11000 FT' (OR SO HE THOUGHT). PNF PUT 11000 FT INTO THE ALT PRESELECT. PNF ASKED PF IF HE HEARD 'R TURN TO 240 DEGS' AND HE SAID DEFINITELY. CLBING THROUGH OR VERY NEAR 10000 FT THE CTLR TOLD US TO CONTACT ZDC ON FREQ (I CAN'T RECALL). PNF CHKED IN OUT OF 10000 FT CLBING TO 11000 FT AND RECALLED LOOKING AT THE ALT PRESELECT TO ASSURE PROPER ALT. ZDC SAID 'ACFT X ROGER; CLBING TO 11000 FT.' HE THEN POINTED US OUT AS POSSIBLE TFC TO AN ACR ACFT THAT WAS DSNDING. THEY SAID THEY HAD US ON THE TCASII BUT NOT IN SIGHT. WE WERE IN AND OUT OF THE TOPS OF CUMULUS CLOUDS THAT TOPPED OUT AROUND 12000 FT. THE PF WAS SLOWING HIS RATE OF CLB IN ANTICIPATION OF CAPTURING 11000 FT AND AROUND 10700 FT ZDC CALLED AND SAID 'VERIFY MAINTAIN 10000 FT.' PNF SAID 'NEGATIVE; WE ARE CLBING TO 11000 FT AS ASSIGNED BY FAY DEP.' HE SEEMED CONFUSED AND SAID WE WERE SUPPOSED TO MAINTAIN 10000 FT AND ASKED TO VERIFY FAY ASSIGNED 11000 FT AND PNF SAID 'YES.' HE THEN SAID TO GO AHEAD AND CLB AND MAINTAIN 11000 FT. WE SAID ROGER AND DID SO. HE MADE ANOTHER TFC CALL TO THE ACR ACFT AND THEN ANOTHER VOICE CAME ON THE FREQ. HE ASKED US IF WE COULD ACCEPT 14000 FT AND PNF SAID YES. HE THEN ISSUED A CLB TO 14000 FT AND DIRECT TO A VOR (NOT LIBERTY VOR). SHORTLY THEREAFTER; WE WERE HANDED OFF TO ZTL. WHEN WE ARRIVED AT GSP; WE WENT AND HAD LUNCH AND DISCUSSED THAT WE MUST HAVE HEARD 11000 FT FROM FAY SINCE WE BOTH HEARD IT AND PNF SET IT IN THE ALT PRESELECT. WE FIGURED IT MUST NOT HAVE BEEN A SEPARATION VIOLATION SINCE HE (THE ORIGINAL ZDC CTLR) TOLD US TO GO AHEAD AND CONTINUE CLB TO 11000 FT. PNF SAID CTLR HAD BEEN REPLACED AND THAT WAS A BAD SIGN AND WE DISCUSSED HOW THIS COULD HAVE HAPPENED (MORE ON THAT LATER). WHEN WE GOT BACK FROM LUNCH; THE FBO AT GSP SAID HE HAD RECEIVED A CALL FROM ZDC ASKING THE PLT TO GIVE THEM A CALL. PNF PLACED THE CALL AND WAS TOLD THERE HAD BEEN A SEPARATION VIOLATION AND THAT HE CHKED THE TAPES AND HE HEARD THE READBACK TO FAY DEP AS '10000 FT' NOT 11000 FT AS PNF AND THE PF THOUGHT. PNF ASKED IF THE ZDC CTLR READ BACK 10000 FT AND HE SAID THE CTLR READ BACK '11000 FT.' PNF ASKED HOW COME WE WERE TOLD TO GO AHEAD AND MAINTAIN 11000 FT AND HE SAID THAT THE SEPARATION HAD ALREADY BEEN VIOLATED AS WE WERE CLBING VERY FAST; (I CLRLY RECALL WE WERE CLBING AT LESS THAN 1000 FPM BTWN 10000 FT AND 11000 FT.) HE SAID HE WAS STILL FIGURING OUT WHAT HAPPENED BUT THAT THE CTLR HAD ERRED AND WE HAD MESSED UP TOO. HE SAID HE WAS FORWARDING THE PAPERWORK TO THE FSDO AND THAT WAS ALL HE COULD DO ONCE THE 'BELLS AND WHISTLES' WENT OFF (I ASSUME HE MEANT THE SNITCH PATCH). HE WISHED ME GOOD LUCK. PF AND PNF WERE DEVASTATED AS WE TAKE OUR FLYING SERIOUSLY. WE WONDERED HOW COULD FAY DEP HAND US OFF IT WE WERE ABOVE OUR ASSIGNED ALT OR IF A SEPARATION VIOLATION EXISTED? AND IF A SEPARATION WAS LOST; HOW COME ZDC TOLD US TO GO AHEAD AND CLB TO 11000 FT? AND HOW DID PNF AND PF MISS THE ORIGINAL CALL TO 10000 FT? FINALLY; PF AND PNF ARE NOW READING BACK 10000 FT AND 11000 FT AS 'ONE-ZERO; TEN THOUSAND' AND 'ONE-ONE; ELEVEN THOUSAND' RESPECTIVELY. ALSO; ONLY THE PNF WILL SET THE ALT PRESELECT AND THEN CALL OUT THE ALT SET AND THE PF MUST POINT TO IT AND SAY THE ALT SET. SAME THING WITH THE AUTOPLT PRESELECT ARMED.