A CANADIAN PACIFIC MCDONNELL DOUGLAS DC-10 (FLT 3), CG-CPJ, & A REEVE ALEUTIAN BOEING 727 (FLT 724), N832, WERE CLRD TO FLY AT FL 290 ON 2 DIFFERENT AIRWAYS. THE AIRWAYS CROSSED AT PICUM INTXN, OVR THE BEARING SEA. WHILE TRAVELING IN NRLY OPPOSITE DRCTNS AT THE SAME ALT, THE 2 ACFT PASSED W/I APRX 1/2 MI OF EACH OTHER, WHERE THE AIRWAYS CROSSED AT PICUM. THE DC-10 CREW SAW THE B-727, BUT THE B-727 CREW DID NOT SEE THE DC-10. PICUM INTXN WAS LOCATED IN AN AREA THAT WAS BYD NORMAL RADIO & RADAR RANGE OF THE ATC CONTROLLERS (CTLRS). THE 2 ON DUTY CTLRS HAD COMBINED SECTORS 10 & 11, THEN HAD DIVIDED THE 2 SECTORS IN A NORTH/SOUTH CONFIGURATION, WHICH WAS CONTRARY TO SOP. THE INCIDENT OCCURRED DRG A BUSY TIME. THE SUPVR WAS HELPING 1 OF THE 2 CTLRS. THE CTLR, WHO WAS HNDLG FLT 3, CLRD IT TO DSCND FM FL 330 TO FL 290 & SAID HE TOLD THE OTHER CTLR TO STOP FLT 724 AT FL 280, WHEN FLT 724 WAS CLIMBING FM A LWR ALT. THE CTLR, WHO WAS HNDLG FLT 724, STATED THAT HE DID NOT KNOW THERE WAS AN ACFT AT FL 290 WHEN HE CLRD FLT 724 TO FL 290.