A C172 INSTRUCTOR PLT DID NOT FULLY HEAR THE RADIO COM BTWN HIS STUDENT AND AN ARTCC RADAR CTLR AND THEREFORE DID NOT DSND TO HIS ASSIGNED ALT.

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I WAS CONDUCTING AN IFR TRAINING FLT IN VISUAL CONDITIONS. I TOLD THE STUDENT TO CONTACT ZSE AND ASK FOR A PRACTICE ILS RWY 16R APCH TO PAE. DUE TO A PROB WITH THE INTERCOM IN THE AIRPLANE; I COULD NOT HEAR WHAT MY STUDENT REQUESTED. THE CTR CTLR REPLIED; 'DID YOU FILE A FLT PLAN?' I THEN RESPONDED WITH 'NO SIR; WE JUST WANT PRACTICE APCHS.' HE THEN ASKED ME TO GIVE HIM EXACTLY WHAT TYPE OF APCHS; HOW MANY OF EACH; AND HOW THE APCHS WILL TERMINATE. I REPLIED; '1 ILS RWY 16R FOLLOWED BY A MISSED APCH; THEN 1 FULL PROC NDB FOLLOWED BY A MISSED APCH; THEN RETURNING TO RENTON FIELD VFR.' HIS REPLY WAS; 'SO YOU WANT IFR; I WILL GET BACK TO YOU.' HE THEN CLRED US TO PAE ARPT VIA RADAR VECTORS; MAINTAIN 3000 FT. AT THE TIME WE WERE AT 3500 FT. A FEW MINS LATER; CTR ADVISED US THAT OUR ASSIGNED ALT WAS 3000 FT. WE WERE STILL AT 3500 FT SO I INSTRUCTED THE STUDENT TO DSND TO 3000 FT. WITH THE CONFUSION CAUSED FROM THE INTERCOM IN THE AIRPLANE AND THE VERY UNHELPFUL CTR CTLR; I ASSUMED THAT WE WERE IN VIOLATION FOR NOT MAINTAINING OUR ASSIGNED ALT OF 3000 FT FOR A FEW MINS UNDER IFR. I BELIEVE THE MAJOR CAUSE FOR MISSING THE ASSIGNED ALT WAS MY BEING UNABLE TO HEAR THE FULL CLRNC DUE TO THE INTERCOM. I SQUAWKED THE PROB TO OUR MECHS ONCE WE LANDED.