ALTDEV ALT OVERSHOT IN NON ADHERENCE TO ATC CLRNC.

Narrative

WE DEPARTED KZTC (TREASURE KEY BAHAMAS) ENRTE TO MCO VFR. CLBING THROUGH 7000 TO 12500 WE RECEIVED OUR IFR CLRNC TO MCO. RNAV DIRECT VRB CLB TO FL200. (ZMA 134.20). PASSING 12000 FT; I TOLD THE FO (PF) I WAS OFF RADIO TO TALK TO THE PAX (COMPANY REQUIREMENT OUT OF 10000 FT; STERILE COCKPIT NOT IN EFFECT). AS I WAS DOING SO; THE FO ADVISED ME HE WAS GOING TO REQUEST 16000 FT AS A FINAL. I SAID OK. I DID THE PA WITH MY ATC RADIO OFF. WHEN I WAS DONE WITH THE PA I TUNED UP MY ATC RADIO AND TOLD THE FO 'I'M BACK.' HE SAID; 'NO CHANGES.' MINUTES LATER; ZMA ASKED US WHAT OUR ALT WAS. I REPLIED 17000 FT CLBING 20000 (20000 WAS SET IN THE ALT SELECTOR). ZMA SAID; DIDN'T YOU REQUEST 16000 FT? I GAVE YOU 16000 FT. WE DSNDED TO 16000 FT. THE FO DID REQUEST 16000; BUT DIDN'T CHANGE THE ALT SELECTOR OR INFORM ME WHEN I SAID; 'I'M BACK;' IN THE CHANGE IN ALT. WE WERE OFF AIRWAY DIRECT VRB; CTLR SAID; 'NO CONFLICT; BUT I THOUGHT YOU WANTED 16000 FT.' THE FO FAILED TO COM THE CHANGE VERBALLY OR BY INDICATING IT WITH THE ALT SELECTOR. I FAILED BY NOT QUESTIONING IT WHEN I RETURNED; AND I NOW MONITOR ATC WHEN I MAKE A PA. AS WELL TRY TO AVOID SINGLE PLT OPS ON THE RADIO.