DURING A DUAL INST FLT IN A SENECA; THE FLT INSTRUCTOR INADVERTENTLY CLBED THROUGH THE ASSIGNED ALT. THE STUDENT HAD INCORRECTLY ENGAGED THE AUTOPLT AND THE INSTRUCTOR WAS CORRECTING THE SIT; BUT ASSUMED THE WRONG ALT. LTSS RESULTED.

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OUR SENECA WAS CLRED TO TIX VIA RADAR VECTORS TO MLB DIRECT CLB AND MAINTAIN 2000 FT; EXPECT 3000 FT IN 10 MINS. I WAS THE INSTRUCTOR. WE DEPARTED VRB ARPT ON AN ASSIGNED HDG OF 290 DEGS AND CLBED TO 2000 FT. MY STUDENT (ON HIS 2ND IFR FLT) WAS FLYING THE ACFT. HE REACHED 600 FT AND CONTACTED ZMA. THIS WAS PREMATURE DUE TO THE FACT THAT CLB PWR WAS NOT SET; THE CLB CHK WAS NOT COMPLETE; AND WE WERE BEGINNING TO DEVIATE FROM OUR HDG. ZMA ASKED US TO IDENT; THEN RPTED US IN RADAR CONTACT AND TOLD US TO MAINTAIN 2000 FT. I READ BACK 'MAINTAIN 2000 FT.' WE WERE THEN GIVEN A HDG OF 300 DEGS (10 DEGS TO THE R). MY STUDENT HAD INCORRECTLY ENGAGED THE AUTOPLT IN A 900 FPM CLB WHICH LEFT OUR AIRSPD BLEEDING OFF. I TOOK CTL OF THE ACFT; DISCONNECTED THE AUTOPLT; REDUCED THE RATE OF DSCNT; AND ATTEMPTED TO READ BACK THE CLRNC. I INCORRECTLY READ BACK A 330 DEG HDG. ZMA THEN CORRECTED US WITH A 300 DEG HDG. I TURNED THE ACFT TO 300 DEGS AND BELIEVED I WAS CLRED TO 3000 FT. I CAN ONLY THINK THAT I MUST HAVE MISTAKEN MY HDG ASSIGNMENT SOMEHOW WITH 3000 FT; OR I JUST ASSUMED I HEARD A 3000 FT ASSIGNMENT BECAUSE THAT IS A COMMON ALT ASSIGNMENT OUT OF VRB (ZMA). AT 2800 FT; WITH THE STUDENT BACK ON THE CTLS; MIAMI ASKED TO VERIFY I WAS MAINTAINING 2000 FT. I READ BACK THAT I WAS CLBING TO 3000 FT. SHE THEN GAVE ME TA FOR OPPOSITE DIRECTION AND TOLD ME TO CLB TO 4000 FT. WHEN I RETURNED FROM THE FLT; I WAS ADVISED THAT MIAMI HAD LOST SEPARATION ON ANOTHER ACFT AND MYSELF DUE TO MY ALTDEV. I BELIEVE THIS DEV TOOK PLACE BECAUSE OF MY FAILURE TO DIVIDE MY ATTN AND SET PRIORITIES. I WAS FRUSTRATED AT MY STUDENT'S INCORRECT PROCS AND INCORRECT USE OF THE AUTOPLT. I WAS TRYING TO CORRECT AN INAPPROPRIATE PITCH ATTITUDE; A HDG DEV; ANSWER THE RADIO CALLS; AND BRIEF MY STUDENT ON WHY I TOOK CTL OF THE ACFT. IN ATTEMPTING TO DO TOO MUCH AT ONE TIME; MY ATTN TO DETAIL SUFFERED; AND I CLBED TO THE INCORRECT ALT. WHEN ISSUED THE NEW CLRNC; I IMMEDIATELY CLBED TO 4000 FT. I LATER CALLED ZMA AND DISCUSSED THE DEV WITH THE SUPVR WHO BRIEFED ME ON THE TAPES AND HIS ASSESSMENT OF THE COMS. LATER I DISCUSSED THE CAUSE OF THE DEV AND THE WAYS TO AVOID ANOTHER DEV WITH THE CHIEF PLT.