FLC OF CL65 HAS MISCOM WITH ATC RESULTING IN LTSS DURING DSCNT. TCASII ACTIVATES.

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ENRTE TO SJC VIA EL NIDO VOR; THEN DIRECT PAPEE INTXN. MY COPLT WENT OFF FREQ TO CALL FBO AND LISTEN TO ATIS. WE WERE IN A DSCNT FROM FL260 TO FL240. CTR GAVE US CLRNC FROM FL240 TO FL230. I ACKNOWLEDGED AND COMPLIED. JUST BEFORE LEVELING AT FL230; MY COPLT CAME BACK ON FREQ WITHOUT ADVISING ME; ACKNOWLEDGED A CALL TO DSND TO 12000 FT; THEN SELECTED 12000 FT IN THE ALT SELECTOR. THE COPLT; MYSELF; AND ANOTHER PLT IN THE JUMP SEAT HEARD A XMISSION OF '12000 FT.' THE NEXT XMISSION WAS THE COPLT VERIFYING A TA GIVEN BY CTR. WE THEN TURNED OUR TCASII TO ON-SCREEN (MFD) AT WHICH POINT WE RECEIVED A TA. THE TFC WAS AT 5 O'CLOCK AND 1800 FT BELOW US. CONTINUING OUR DSCNT; CTR THEN XMITTED ASKING US OUR ALT. WE REPLIED FL210 AND DSNDING TO 12000 FT. HE THEN TOLD US WE WERE NOT CLRED TO DSND. WE ASKED TO LEVEL AT FL210. CORRECTIVE ACTION: WHENEVER ONE PLT LEAVES OPERATING FREQ; HE NEEDS TO STATE SO. WHEN RETURNING; HE ALSO NEEDS TO STATE SO; THEN SHOULD BE BRIEFED BY PF AS TO ANY CHANGES OR CONDITION OF FLT. IN THIS INSTANCE; ALL 3 PLTS HEARD 12000 FT. WHETHER IT CAME FROM THE COPLT OR ORIGINATED ELSEWHERE; THE COPLT ACKNOWLEDGED 12000 FT. IF UNCERTAINTY IS FELT; ALWAYS DOUBLECHK WITH CTLR. UNFORTUNATELY; IN THIS INSTANCE; ALL 3 PLTS HEARD 12000 FT. SUPPLEMENTAL INFO FROM ACN 405555: ATC CALLED US BACK AS WE WERE DSNDING THROUGH FL210. WE THEN HELD FL210 AND WERE THEN ASKED TO CALL THE CTR.