FLC OF A B727 OVERSHOT DSCNT ALT DUE TO BELIEVING THAT THEY WERE CLRED TO A LOWER ALT THAN ACTUALLY GIVEN. ARTCC RADAR CTLR INTERVENED AND ADVISED THAT THEY HAD PASSED THEIR ASSIGNED ALT AND TO GO BACK TO IT. ALL 3 FLC MEMBERS THOUGHT THAT THEY HAD HEARD THE LOWER ALT AND THE CAPT READ IT BACK TO THE CTLR.

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WE WERE CRUISING AT FL350 AND WERE WITH ZID ON 128.77. I WAS FLYING AND THE CAPT WAS WORKING THE RADIOS. AT APPROX XX50Z WE WERE CLRED TO DSND TO WHAT WE THOUGHT WAS FL230. THE CAPT READ BACK OUR DSCNT CLRNC TO THE CTLR AS FL230. HE SET FL230 IN THE AWI AND WE BOTH ACKNOWLEDGED IT. AS I DSNDED THROUGH APPROX FL315; THE CTLR RPTED THAT HE HAD CLRED US TO FL330 AND TO CLB BACK TO AND MAINTAIN FL330. THE CAPT ACKNOWLEDGED AND WE CLBED BACK UP TO FL330. ALSO; PRIOR TO THIS INCIDENT; THE CAPT COMMENTED TO THE CTLR THAT SOMETIMES HIS XMISSIONS WERE CUT OFF AT THE END. HE COMMENTED ON THIS AGAIN; AFTER THE OCCURRENCE; AS THE CTLR'S XMISSIONS WERE STILL SOMETIMES CUT OFF AT THE END. WE DID NOT RECEIVE ANY TCASII ALERTS AND THE CTLR DID NOT SAY WE HAD VENTURED CLOSE TO ANY OTHER ACFT. I BELIEVE WE HAD BECOME A LITTLE DISTR BY THE DETERIORATING WX AT OUR DEST OF DTW. (WE ENDED UP SHOOTING A CAT II APCH.) BUT ALL 3 OF US (CAPT; FO; AND SO) THOUGHT WE HEARD FL230. IN THE FUTURE; I PLAN TO PAY MUCH CLOSER ATTN TO ALL ATC INSTRUCTIONS AND VERIFY; IF THERE IS ANY DOUBT.