AFTER CLBING TO FL230; A B737 CREW LEARNS THEY HAD ONLY BEEN CLRED TO FL210.

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I JOINED THE CAPT AT XXX TO FLY A RESERVE PAIRING: XXX TO XXX TO XXX. THIS WAS MY LEG TO FLY. GND OPS; TKOF; AND INITIAL DEP WERE NORMAL. PROCEEDING E FROM XXX; WE WERE SWITCHED TO ZAU (FREQ 127.55). CTR THEN CLRED US TO CLB FROM AN INTERMEDIATE ALT TO A HIGHER ALT. I WAS FLYING THE ACFT AND DO NOT RECALL HEARING THE ALT ASSIGNED BY CTR. HOWEVER; THE CAPT (PNF) ACKNOWLEDGED THE CALL; READING BACK THAT WE WERE CLRED TO FL230. HE THEN ENTERED 23000 FT INTO THE MCP ALT WINDOW. I THEN POINTED AT THE WINDOW AND ACKNOWLEDGED 'FL230.' AT APPROX XA00; I BEGAN LEVELING OUT OF FL230. AT THIS TIME; CTR ASKED; 'AT WHAT ALT ARE YOU GOING TO STOP YOUR CLB?' THE CAPT REPLIED THAT WE WERE FILED TO FL230; AND THAT ALT WAS FINE FOR US. AFTER HIS ANSWER; AND NO REPLY FROM CTR; WE DISCUSSED IN THE COCKPIT; THINKING THAT WAS AN UNUSUAL QUESTION FROM CTR. THE CAPT THEN ASKED CTR IF FL230 HAD BEEN OUR ASSIGNED ALT. CTR THEN REPLIED THAT WE HAD BEEN CLRED TO FL210. THE CAPT THEN QUERIED AS TO WHETHER A RPT WAS REQUIRED; AND THE CTLR RESPONDED; 'NO.' BOTH THE CAPT AND I DECIDED TO SUBMIT ASAP RPTS ANYWAY (INCIDENT OCCURRED APPROX 50 NM W OF LFD). WHILE I AM NOT POSITIVE REGARDING THE ALT SPECIFIED IN CTR'S INITIAL ALT ASSIGNMENT RADIO CALL; I AM CERTAIN THAT THE CAPT READ BACK A CLRNC TO FL230; ENTERED IT CORRECTLY INTO THE MCP ALT WINDOW; AND THAT I ACKNOWLEDGED HIS READBACK AT FL230. IF HIS READBACK WAS INCORRECT; CTR DID NOT NOTE THE INCORRECT READBACK OR OFFER A CORRECTION. RECOMMENDATION: CLOSER MONITORING BY BOTH PLTS OF ALL ATC XMISSIONS; QUERYING THE CTLR IF UNCERTAIN AS TO THE CLRNC; AND BETTER MONITORING OF PLT CLRNC READBACKS BY ATC CTLR.