FLC ON DC9 DEP OFF IAD FELT ATC WAS CONFUSED WITH THEIR CLBOUT. WHILE IN A R TURN; FLC SPOTTED A COMMUTER ACFT ON THEIR R THAT APPARENTLY HAD DEP OFF THE R PARALLEL RWY.

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WE DEPARTED THE GATE AT WASHINGTON DULLES ARPT AT XA05Z ON JUN/FRI/98. WE WERE CLRED FOR TKOF ON RWY 19L WITH NO ASSIGNED HEADING AND ON THE CAPITOL FOUR DEP; CLBING TO 4000 FT. AFTER HDOF TO DEP CTL WE WERE INSTRUCTED TO FLY A 320 DEG HDG AND CLB TO 11000 FT. I BELIEVE WE WERE ALSO INSTRUCTED TO INTERCEPT J-149 OFF AML. WHILE IN THE R TURN WE ESTABLISHED VISUAL CONTACT WITH A TURBOPROP COMMUTER AT OUR 2-2:30 O'CLOCK POS; AND IT APPEARED THAT ACFT HAD DEPARTED RWY 19R. WHILE IN THE TURN; DEP CTL CALLED AND ASKED OUR HEADING. MY COPLT'S RESPONSE WAS 'TURNING TO HDG 320 DEGS; TFC IN SIGHT.' SHORTLY AFTER THAT DEP CALLED BACK AGAIN AND ASKED FOR OUR HEADING; AND THIS TIME MY COPLT SAID FORCEFULLY 'TURNING TO HDG 320 DEGS; TFC IN SIGHT.' DEP CTL THEN SAID 'TFC AT 12 O'CLOCK POS LEVEL OFF AT 4000 FT.' WHILE DOING THAT WE RECEIVED A TCASII RA. SHORTLY AFTER PASSING BEHIND TFC WE WERE INSTRUCTED TO TURN TO A 240 DEG HDG WHICH WAS IN THE DIRECTION OF THE TFC WE HAD JUST PASSED. SHORTLY THEREAFTER WE WERE ASSIGNED A NORTHWESTERLY HEADING AND INSTRUCTED TO CLB TO 11000 FT AND INTERCEPT J-149 OFF AML. AT NO TIME WERE WE GIVEN ANY INSTRUCTIONS TO LET US KNOW THERE WAS TFC OR THAT WE SHOULD MAINTAIN VISUAL CONTACT WITH ANY TFC. WE WERE NEVER ADVISED THAT WE HAD DONE ANYTHING WRONG. IT SEEMED THAT DEP CTL WAS VERY CONFUSED ABOUT WHAT WAS HAPPENING REGARDING SPACING. I AM NOT CERTAIN THAT THEY WERE SATISFIED WITH THEIR RADAR SEPARATION; EVEN THOUGH WE ALWAYS HAD SAFE SEPARATION VISUALLY. THE REMAINDER OF THE FLT WAS UNEVENTFUL.