ZDC RADAR CTLR INCORRECTLY ASSIGNS AN ACR AN ALT CONFLICTING WITH A MIL C130. CTLR THOUGHT HE ASSIGNED AN ALT 1000 FT BELOW THE C130.

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MIL C130 (ACFT X) SBOUND AT FL190. ACR Y WAS WBOUND CLBING TO 17000 FT (LOOKING FOR FL200). I THOUGHT I CLBED ACR Y TO FL180. I CALLED TFC AND BOTH ACFT HAD EACH OTHER IN SIGHT. I ACTUALLY HAD CLBED ACR Y TO FL190. I MISSED THE READBACK. WHEN CONFLICT ALERT WENT OFF; I VERIFIED THE ASSIGNED ALT; AND THEN DSNDED ACR Y BACK TO FL180. I KNOW I MADE A MISTAKE. I WISH; HOWEVER; THAT THE PLTS WOULD HAVE QUESTIONED ME AS I CALLED TFC. SUPPLEMENTAL INFO FROM ACN 420592: THE RADAR CTLR THOUGHT HE HAD ASSIGNED FL180. WHEN THE RADAR CTLR NOTICED ACR Y LEAVE FL180 ON THE DATA BLOCK; HE READ THE PLT THE ALTIMETER. THE PLT STATED HE WAS CLBING TO FL190. THE RADAR CTLR ASSIGNED FL180 TO THE PLT. SUPPLEMENTAL INFO FROM ACN 420581: ZDC CLRED US TO CLB TO FL190 AND TURN TO HDG 290 DEGS. AS WE PASSED ABOUT 17000 FT; HE POINTED OUT C130 TFC AT FL190 AT 2 O'CLOCK. I SAW IT AS IT PASSED ABOUT OUR 2:30 - 3 O'CLOCK POS AND WATCHED IT PASS BEHIND US ON TCASII AT ABOUT 3 MI. AS WE PASSED ABOUT FL183; THE CTLR TOLD US THE LCL ALTIMETER SETTING. I WONDERED WHY WE NEEDED THAT INFO ABOVE FL180; SO I SAID SOMETHING LIKE; 'ROGER; BUT WE'RE CLBING TO FL190.' HE SAID SOMETHING LIKE; 'NEGATIVE; YOUR CLRNC IS FL180!' I SAID 'WE READ BACK FL190; BUT WE'LL DSND BACK TO FL180.' NO IMMEDIATE COMMENT FROM ATC. SO WE STARTED A DSCNT TO FL180 AS WE APEXED OUR CLB AT FL185. SHORTLY THEREAFTER ATC CLRED US TO OUR CRUISE ALT OF FL200. I NOW THINK I SHOULD HAVE ASKED HIM WHY THE C130 AND US WERE EVENTUALLY GOING TO BE AT FL190 WITHIN 10 MI AND/OR WAS THERE GOING TO BE A CONFLICT. THAT QUESTION WOULD HAVE CLRED UP THE OBVIOUS FLT LVL CLRNC DISCREPANCY EARLY ON.