AN MLG FLC; WITH AN ACI ON BOARD; CLBS ABOVE THEIR ASSIGNED ALT WHEN THEY BECOME DISTRACTED DURING AN APCH RWY CHANGE.

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WE WERE BEING VECTORED FOR ILS RWY 23L BEHIND A SINGLE ENGINED ACFT; WE WERE AT MINIMUM AIRSPD AND RECEIVED 2 VECTORS THROUGH FINAL APCH COURSE AS CTLR TRIED TO MAINTAIN SPACING. AT FAF CTLR BROKE US OFF THE APCH. WE COMPLIED WITH NBOUND TURN AND CLB TO 3000 FT. AT 3000 FT WE WERE GIVEN ANOTHER TURN; CLB 3200 FT AND EXPECT VECTORS RWY 23R ILS. I STARTED A SLOW CLB 3200 FT. AT THIS POINT CREW HAD CONFUSION OVER ASSIGNED HEADING. I MISSED THE LEVELOFF AT 3200 FT; CAUGHT AND CORRECTED ALT AT 3400 FT. REST OF PATTERN AND APCH WAS UNEVENTFUL. AFTER LNDG A FAA INSPECTOR IN JUMP SEAT MENTIONED THE ALT. BOTH CAPT AND MYSELF WERE IN AGREEMENT THAT ASSIGNED ALT WAS 3200 FT. FAA INSPECTOR THOUGHT IT WAS 3000 FT. NOTHING ELSE WAS SAID AND INSPECTOR LEFT THE ACFT. FACTORS CAUSING THE POTENTIAL ALTDEV WERE COMPLYING WITH GAR INSTRUCTIONS; QUICK CHANGES TO HEADING; ALT AND EXPECTED APCH; AND CONFUSION OVER HEADING (DISTR) DURING A SMALL ALT CHANGE (200 FT). I BELIEVE 'LESS THAN IDEAL' APCH CTLING TO A LOW WX (500/1) APCH GREATLY INCREASED WORKLOAD DURING A CRITICAL PHASE OF FLT.