DESCENDED BELOW ASSIGNED ALT. AIRBORNE CONFLICT.

Narrative

WHILE CONDUCTING APCH TO RWY 19R ATC SAID TO MAINTAIN 3500' AND TO RPT ESTABLISHED ON THE APCH. AFTER BEING ESTABLISHED ON THE APCH; I RPTED 'ESTABLISHED ON ILS 19R APCH.' ATC APCH ACKNOWLEDGED. I THEN BEGAN A DSCNT ACCORDING TO THE PUBLISHED APCH PROC AND LEVELED OFF AT 3000'. PRIOR TO BEING ESTABLISHED; TFC WAS CALLED OUT AT OUR 7 O'CLOCK POS AND OVERTAKING US. OTHER TFC RPTED VISUAL CONTACT WITH US. TFC PASSED BELOW US AT ABOUT 200'; BELOW OUR ALT FROM 7 TO 2 O'CLOCK POSITIONS. WE FIRST SAW ACFT WHEN IT REACHED OUR 2 O'CLOCK POS. NO MANEUVERING WAS REQUIRED BY EITHER ACFT. UPON LEVELING OFF AT 3000'; APCH CALLED US AND INFORMED US THAT THEY HAD NOT GIVEN US PERMISSION TO DSND BELOW 3500'. I FEEL THIS INCIDENT OCCURRED BECAUSE OF CONFUSION BTWN BEING ESTABLISHED ON THE APCH AND BEING CLRED FOR THE APCH. IT WOULD HAVE HELPED IF ATC HAD REPEATED TO MAINTAIN 3500' UNTIL CLRED FOR THE APCH; OR UNTIL FURTHER NOTICE. AT THE TIME; I RPTED ESTABLISHED ON ILS 19R APCH. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING: INDICATES PLT IN TRNING FOR INSTRUMENT RATING; UNDER HOOD; NEVER SAW THE OTHER ACFT. NO EVASIVE ACTION TAKEN. LEARNED NEED TO LISTEN CAREFULLY TO CTLR PHRASEOLOGY.