CREW ALLEGEDLY MISINTERPED A DSCNT CLRNC CAUSING A PLANNED LEVELOFF AT WRONG ALT.

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I WAS THE FO AND PF ON ACR FLT XXX FROM ATL TO IAD; LEVEL AT FL230 ON J51 BTWN CREWE AND FAK. ATC CLRED US TO DSND TO FL200. I ENTERED FL200 IN THE ALT WINDOW OF THE MCP AND INITIATED A 1000 FPM DSCNT WITH THE AUTOPLT ON. THE CAPT (PNF) READ BACK THE CLRNC AS 'FLT LEVEL TWO ZERO ZERO' AND POINTED AT THE MCP ALT WINDOW TO CONFIRM THE CORRECT SETTING; PER COMPANY PROCS. I STOPPED THE DSCNT AND THE CAPT QUESTIONED ATC TO CONFIRM OUR ALT ASSIGNMENT. ATC THEN AMENDED THE CLRNC AS 'MAINTAIN FL210.' I ENTERED FL210 IN THE ALT WINDOW OF THE MCP AND THE CAPT READ BACK 'FLT LEVEL TWO ONE ZERO.' THE AUTOPLT CAPTURED AND LEVELED OFF AT FL210. ATC THEN CLRED US TO 'TURN R HDG 090 DEGS FOR TFC.' I TURNED TO THE NEW HDG AND THE CAPT READ BACK THE CLRNC. THE CAPT QUESTIONED ATC ABOUT THE ALT CONFUSION AND ATC SAID HE BELIEVED WE WERE ORIGINALLY CLRED TO FL220; BUT HE WOULD HAVE TO PULL THE TAPES TO BE SURE. HE ALSO SAID THE OTHER ACFT WAS 'HURRIED DOWN' AND THERE WERE NO SEPARATION PROBS. HE THEN CLRED US TO NEW HDG 360 DEGS TO REJOIN OUR FLT PLANNED RTE. THERE WERE NO TCASII ALERTS IN OUR ACFT. THE CAPT AND I DISCUSSED THE SEQUENCE OF EVENTS AND WE BOTH BELIEVE THE ORIGINAL CLRNC WAS FOR FL200 AND ATC MADE A MISTAKE. ATC MAY HAVE INTENDED TO SAY FL220; BUT DID NOT SAY IT AND DID NOT CORRECT THE CAPT WHEN HE READ BACK FL200. I BELIEVE THAT ATC SHOULD BE REQUIRED TO LISTEN FOR AND HEAR A CORRECT READBACK OF ALT CLRNCS. PLTS ARE REQUIRED TO READ THEM BACK FOR A REASON.