ACR MLG OVERSHOT ALT ON DESCENT.

Narrative

I WAS FLYING THE ACFT HDG 180 DEGS; ALT 5000' MSL. F/O MISSED FIRST CALL FROM NY APCH FOR A LEFT TURN TO 140 DEGS AND MAINTAIN 3000' MSL. I DIRECTED THE F/O TO ANSWER; WHICH HE DID WITH THE 140 DEG HDG. I INITIATED THE DSCNT TO 3000' MSL. PASSING APPROX 4400' MSL; NY APCH ADVISED US 5000' MSL ASSIGNED; LEVEL AT 4000' MSL; TFC AT 2 O'CLOCK 3000'; AN SMA NBND. S/O RECALLS DSCNT TO 3000' MSL. F/O DIDN'T UPDATE ALT ALERTER TO 3000' MSL; NOR READ BACK 'MAINTAIN 3000';' BUT DID QUERY ME ABOUT ALT JUST PRIOR TO NY APCH CTL'S CALL. HE ADMITTED MISSING THE FIRST CALL COMPLETELY. PROB COULD HAVE BEEN AVERTED HAD I ANSWERED THE NY APCH CTL MYSELF WITH HDG 140 DEGS AND MAINTAIN 3000' OR ASSUMED THE F/O HAD RESPONDED WITH HDG AND ALT. S/O SHOULD HAVE CONFIRMED THE ASSIGNED HDG AND ALT AFTER F/O MISSED THE FIRST CALL. SUPPLEMENTAL INFO FROM ACN 95943: AS PNF I RESPONDED TO APCH'S ORDER TO DSND TO 5000' AND TO TURN LEFT TO A HDG OF 140 DEGS MAGNETIC. I CALLED OUT OF 6000' AND THE NEXT THING I REALIZED WAS THAT WE WERE DSNDING THROUGH 4700'. I CALLED THIS TO CAPT'S ATTN; THAT WE WERE CLRED TO 5000'. HE THOUGHT WE WERE CLRED TO 3000'. CTLR SAW OUR ALT AND SAID WE WERE TO MAINTAIN 5000'; BUT THEN SAID DSND TO 4000'.