AN EMB145 FLC DSNDS BELOW THEIR ASSIGNED ALT WHILE THE PIC PF IS OFF ON A PA ANNOUNCEMENT ON J34 WITH ZOB; OH.

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AS PART OF A SCHEDULED FAR PART 121 FLT; WE WERE TALKING TO ZOB ON FREQ 135.72. WHILE AT FL250 WE ENCOUNTERED MODERATE TURB AND CHOP. WE ASKED FOR RIDE RPTS FROM ARTCC. FL210 WAS RPTED SMOOTH SO WE REQUESTED FL210. OUR INITIAL CLRNC WAS TO FL240. IT WAS MY LEG AND I INITIATED THE DSCNT TO FL240 THEN WENT OFF COM #1 (ATC) TO MAKE A PA ABOUT OUR RIDE CONDITIONS AND WHAT TO EXPECT AHEAD. THE FO NOW HAD CTL OF THE ACFT AND RADIOS. THE PROB AROSE WHILE MAKING MY PA. THE FO MOTIONED THAT ARTCC CLRED US TO FL210 AND HAD ALSO DIALED FL210 INTO THE ALT PRESELECTOR. NOW WELL INTO THE DSCNT; I JOINED BACK UP ON COM #1 (ATC) THROUGH ABOUT FL240 AND CONFIRMED WITH THE FO THAT WE WERE CLRED TO FL210. WE DISCOVERED THE PROB AT APPROX FL227 WHEN ARTCC QUERIED OUR ASSIGNED ALT. I REPLIED FL227 FOR FL210 AS I UNDERSTOOD WE WERE CLRED. ARTCC SAID WE WERE CLRED TO FL240 ONLY. I STOPPED THE DSCNT INSTANTLY AND STARTED A CLB BACK TO FL240 WHILE SIMULTANEOUSLY COMMUNICATING THIS TO ARTCC. ARTCC THEN CLRED US TO FL210. THE FO HAD OBVIOUSLY MISUNDERSTOOD THE CLRNC WHICH NOW CREATED CONFUSION ON MY BEHALF. WE DSNDED TO FL210. I WAS WORKING THE RADIOS AND ACFT AT THIS POINT AND VERIFIED OUR ACTUAL CLRNC WITH ARTCC. CONTRIBUTING FACTORS INCLUDE AN INTERCOM SYS WHERE A PLT CANNOT MONITOR A COM WHILE TALKING ON ANOTHER COM OR PA; OR EVEN HEAR INTERCOM CONVERSATION FROM THE OTHER PLT WHILE A PUSH-TO-TALK OR MIKE BUTTON IS DEPRESSED. WE WERE BOTH WEARING HEADSETS AT THE TIME AND THE SPEAKERS WERE OFF. OTHER FACTORS INCLUDE THE FO NOT UNDERSTANDING THE ALT CLRNC AND PERHAPS MY FAILURE TO CONFIRM THE CLRNC IN A TIMELY MANNER WITH ARTCC SINCE I DID NOT HEAR IT MYSELF. THE FO IS NEW WITH OUR COMPANY AND AIRPLANE AND MAY HAVE NOT BEEN ENTIRELY COMFORTABLE IN HIS SURROUNDINGS. HE MADE NO MENTION TO ME ABOUT HIS FEELINGS EVEN THOUGH I BRIEFED HIM TO SPEAK UP ANY TIME HE HAD A QUESTION OR FELT UNCOMFORTABLE. FATIGUE WAS NOT AN ISSUE. I BELIEVE HIS ACTIONS; OR LACK OF ACTION COULD POSSIBLY RESULT IN A VIOLATION OF MYSELF AS THE PIC. TO SUMMARIZE; I BELIEVE THE FACTORS THAT LED TO THIS EVENT COULD HAVE BEEN AVOIDED WITH BETTER CREW COMS -- INCLUDING AN INTERCOM SYS THAT ALLOWS MONITORING AND XMITTING ON DIFFERENT COMS AT THE SAME TIME. THE FO'S EXPERIENCE LEVEL; AND A VERIFICATION AND/OR CLARIFICATION OF OUR ALT CLRNC. SUPPLEMENTAL INFO FROM ACN 503560: THE CAPT TURNED ON THE FASTEN SEATBELT SIGN AND RPTED THE TURB TO ATC. HE INQUIRED ABOUT CONDITIONS AT LOWER ALTS. CTR RPTED THAT THE RIDE SMOOTHED OUT AROUND FL210. THE CAPT REQUESTED 'LOWER.' (THIS IS THE POINT WHERE I BELIEVE THE ERROR STARTED.) THE CAPT SET FL240 IN THE FLT GUIDANCE CTLR. HE THEN SAID; 'I'LL BE IN THE BACK; YOU'VE GOT 1.' MEANING THAT HE WAS GOING TO TALK TO THE PAX WHILE I MONITORED ATC ON COM #1. THE PROB AROSE IN THAT I 'BELIEVED' WE WERE CLRED DOWN TO FL210 AND THAT THE APT MERELY DID NOT SET THE ALT CORRECTLY. WE WERE DSNDING AT APPROX 1000 FPM TOWARD FL240 FROM FL250 WHEN I RESET THE ALT SELECT TO FL210. THE CAPT WATCHED ME DO THIS WHILE HE WAS MAKING HIS PA. HE NODDED TO ME BECAUSE HE BELIEVED I WAS GIVEN THIS CLRNC AS I WAS WORKING COM #1. I BELIEVED WE WERE ORIGINALLY GIVEN FL210 (WHICH WE WERE NOT). WE HAD DISCUSSED THAT ALT WITH ATC; BUT WERE NEVER CLRED TO IT. DURING THE POSTFLT; WE DISCUSSED THE PROB AND THE NECESSITY/IMPORTANCE OF XCHKING ALT ASSIGNMENTS AS WELL AS QUERYING 'ANY' OTHER UNCERTAINTIES.