ZDC CTLR ISSUES CORRECTIVE TURNS WHEN A320 OVERSHOOTS ALT ASSIGNMENT BUT SEPARATION IS LOST WITH A CRJ.

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ACFT X; A320; DEPARTED PHL; SBOUND ROUTING OVER SBY. ACFT CHKED ONTO MY FREQ CLBING TO FL280. THIS WAS CONFIRMED BY ANALYZING ARTCC VOICE TAPE. ACFT Y; CRJ1; WAS NBOUND; LEVEL AT FL290; ALSO ROUTED OVER SBY. ACFT X WAS ONLY CLRED TO FL280 BECAUSE ACFT Y WAS CONFLICTING TFC; OPPOSITE DIRECTION. ACFT X PLT ADVISED ME THAT HE WAS REQUESTING FL300 IF THE 'RIDES' WERE SMOOTH. I ACKNOWLEDGED HIS REQUEST AND STATED THAT WE WOULD WORK ON GETTING HIM THE REQUESTED ALT AFTER SBY; WHICH IS WHEN ACFT X AND ACFT Y WOULD BE CLR OF EACH OTHER. WHILE PERFORMING OTHER DUTIES IN A BUSY; COMBINED SECTOR; AN ACFT CALLED REQUESTING CONFIRMATION OF ASSIGNED ALT. AS THE CALL SIGN WAS SCRAMBLED; I ASKED FOR A REPEAT. ACFT X ASKED TO CONFIRM THAT HE WAS CLRED TO FL300. AT THIS POINT; ACFT X WAS SHOWING A RPTED ALT OF FL280. ACFT Y WAS LEVEL AT FL290; HEAD-ON AND 5 MI OR LESS FROM EACH OTHER. I CLRED ACFT X TO MAINTAIN FL280 AND TURNED ACFT TO A 180 DEG HDG; A TURN OF APPROX 40 DEGS. I THEN CLRED ACFT Y TO TURN L TO A 330 DEG HDG; A TURN OF APPROX 55 DEGS. ACFT Y REPLIED THAT HE WAS TURNING '30 DEGS L' AND WAS DSNDING IN RESPONSE TO A TCAS RA. A MOMENT LATER; ACFT X REPLIED THEY WERE RESPONDING TO A TCAS RA. ONCE ACFT WERE CLR OF EACH OTHER; I RECLRED BOTH ACFT BACK ONTO THEIR RTES AND REASSIGNED ALTS. ACFT Y REPLIED 'THAT WAS CLOSE' AND ACFT X REPLIED THEY WERE GOING TO FILE AN NMAC RPT. ZDC QUALITY ASSURANCE OFFICE ANALYSIS OF THE EVENT SHOWED THAT ACFT X WAS ONLY CLRED TO FL280 AND THE PLT DEVIATED FROM HIS ASSIGNED ALT; CAUSING THE EVENT. SUPPLEMENTAL INFO FROM ACN 735599: WE WERE CRUISING AT FL280 AND GOT CLRNC TO FL300. WE GOT A TA FOLLOWED BY AN RA AND CTR ASKING US TO TURN L TO 180 DEGS. THE OTHER ACFT GOT A CLRNC TO TURN L TO 270 DEGS. HE WAS AT FL290. WE FOLLOWED RA TO 'CLR OF CONFLICT.' THEN CLBED BACK UP TO FL280 AND ON COURSE.