BE76 INSTRUCTOR PLT DEP FROM TPA RESPONDS TO TFC INFO AND CLBS TO ALT OF CONFLICTING ACR ACFT.

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WE PICKED UP OUR IFR CLRNC AT TPA. THE CLRNC READ: 'CLRED TO FPR AS FILED. TURN HDG 060 DEGS ON DEP AND CLB; MAINTAIN 1600 FT; EXPECT 5000 FT IN 10 MINS.' THE WX AT TPA WAS VFR WITH GOOD VISIBILITY; AND A FEW SCATTERED CLOUDS AROUND 3000-4000 FT. WE TOOK OFF RWY 36R AND TURNED 060 DEGS AND WERE HANDED OFF TO 119.9; AND PASSING 1400 FT WE WERE ASSIGNED 4000 FT; WHICH I READ BACK. WHEN ON THIS HDG AND ALT; THE CTLR CALLED TFC (AN A320) N OF US 5000 FT. I REPLIED TO THE CALL WITH; 'CLB; MAINTAIN 5000 FT' AND I GOT NO REPLY. A COUPLE OF SECONDS AFTER; I CALLED THE TFC IN SIGHT; HAVING JUST LEFT 4000 FT. AT THIS TIME; THE TFC DID NOT LOOK CONFLICTING; SO WE CONTINUED THE CLB. AT 4500 FT; I COULD SEE THAT THE TFC WOULD CONFLICT; AND I LEVELED OFF TO CONFIRM WITH ATC. JUST BEFORE I GOT THE CALL IN; THE CTLR CALLED US AND ASKED WHAT ALT WE WERE AT. I REPLIED '4500 FT; CLBING 5000 FT AS ASSIGNED.' THE CTLR REPLIED THAT 5000 FT WAS NOT OUR ASSIGNED ALT. AT THIS STAGE; OUR ACFT WAS ALREADY IN A DSCNT DOWN TO 4000 FT. IT WAS OBVIOUSLY THE COM THAT FAILED IN THIS INCIDENT. I THINK WHAT MADE MY REPLY 'CLB; MAINTAIN 5000 FT' WAS BECAUSE I EXPECTED IT AS A RESULT OF THE IFR CLRNC. I'M SURE THAT IF THE TFC HAD BEEN CALLED AS 'TFC 11 O'CLOCK POS 1000 FT ABOVE' I WOULD NOT HAVE MISTAKEN THE CALL. I SHOULD DEFINITELY HAVE QUERIED THE CLB BEFORE LEAVING 4000 FT. THE CTLR'S FAILURE TO QUERY MY READBACK MADE ME CONTINUE WITH THE CLB. BY ME DOING THE RADIOS FOR MY STUDENT (BEING UNDER THE HOOD); I SHOULD ALSO MAKE SURE MY STUDENT COPIES AND UNDERSTANDS THE RADIO CALLS BEING MADE AND RECEIVED. SUPPLEMENTAL INFO FROM ACN 637136: BE76 DEPARTED TPA AND WAS IDENTED AND CLBED TO 4000 FT. HE BUSTED HIS ALT AND CONFLICTED WITH AN A320; DSNDING TO 5000 FT.