A B757 FLC EXPERIENCES A POTENTIAL CONFLICT WITH AN OPPOSITE DIRECTION MD80 PROGRAMMED TO CLB THROUGH THEIR ALT NE OF SEA; WA.

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MD80 DEPARTED RWY 34R APPROX 1 MIN AHEAD OF US AND APPEARED TO TAKE UP AN INITIAL HEADING OF 320 DEGS. WE DEPARTED BLUIT THREE FMS DEP. DEP CTL QUERIED IF WE HAD VISUAL ON THE MD80. ACKNOWLEDGED 'YES' AND TOLD TO MAINTAIN VISUAL SEPARATION. AS WE BOTH CLBED TOWARDS 10000 FT; THE MD80 WAS GIVEN A TURN TO THE S (165 DEGS OR SO). WE WERE NOW HEADING 101 DEGS ON THE FMS DEP. THE MD80 CONFIRMED VISUAL ON US AS WELL. WE WERE CLRED TO 15000 FT AND THE MD80 TO 11000 FT OR 12000 FT. AS THE MD80 TURNED TOWARD US; VISUALLY AND TCASII IN SIGHT; I DISCONNECTED THE AUTOPLT AND STARTED A LEVELOFF AT APPROX 10300 FT. IMMEDIATELY THEREAFTER; WE GOT A TCASII WARNING TO 'DSND.' THE MD80 FLEW OVER US APPROX 700 FT AND PERHAPS SLIGHTLY BEHIND US. IN RETROSPECT; DID NOT EXPECT THAT ACCEPTING 'VISUAL SEPARATION' WOULD MEAN THAT DEP CTL WOULD GIVE US SIMILAR ALTS TO CLB TO; OR THAT CONFLICTING HEADINGS WOULD BE ENCOUNTERED. COMPLICATING FACTOR WAS DIFFICULTY IN REALLY UNDERSTANDING POS OF THE MD80 (WELL-LIT WITH HIS LIGHTS ALL ON) AT NIGHT. TCASII GAVE BEST PICTURE. THE SOUTHERLY TURN GIVEN TO THE MD80 REALLY GOT MY ATTN. THE FO AND I HAD GOOD 'SITUATIONAL AWARENESS;' STARTED A DSCNT PRIOR TO TCASII WARNING; BUT I WON'T BE PUT IN THAT SIT AGAIN.