FLC OF A B757 DECLARED AN EMER AND RETURNED TO LAND DUE TO AN ILL PAX. DURING THE RETURN; THE CREW DSNDED PREMATURELY FROM THEIR TRANSITION ALT FOR A VISUAL APCH CAUSING A POTENTIAL CONFLICT WITH ANOTHER ACFT.

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I WAS CAPT OF THE FLT RETURNING TO DFW WITH A MEDICAL EMER. MY FO WAS FLYING THE ACFT. WE HAD A MIDDLE AGED LADY WHO HAD LOST CONSCIOUSNESS AND WAS HAVING DIFFICULTY BREATHING. FROM THE TTT 285/120 ZFW GAVE US PERMISSION TO FLY DIRECT TO JIFFY; THE NDB FOR RWY 17R. REGIONAL APCH CLRED US DOWN TO 3400 FT AS WE WERE XING THE APCH PATH FOR RWY 18R. APCH ASKED US IF WE HAD THE ARPT IN SIGHT. I REPLIED THAT WE DID AND LOOKED DOWN TO FINISH THE APCH CHKLIST WHEN OUR ALT ALERT SOUNDED. THE FO THOUGHT WE HAD BEEN CLRED FOR THE VISUAL APCH AND DSNDED TO 3000 FT. APCH ASKED IF WE HAD THE ACR Y FLT BELOW US AT 2300 FT AT OUR 9 O'CLOCK POS. WE REPLIED THAT WE DID AND WOULD REMAIN AT 3000 FT. SINCE WE WERE ALREADY HIGH FOR THE APCH AND HAD TO LAND; WE DIDN'T WANT TO CLB BACK UP TO 3400 FT. ACR Y SAID THEY HAD US IN SIGHT AND WOULD MAINTAIN VISUAL SEPARATION. THERE WAS NO TCASII ALERT. I SPOKE WITH APCH CTL ON THE PHONE AFTERWARDS AND THEY SAID THERE WASN'T A CONFLICT; ESPECIALLY SINCE WE WERE OBVIOUSLY VERY BUSY DEALING WITH AN EMER RETURN TO DFW.