LEAR 45 FLIGHT CREW RELUCTANTLY ACCEPTS A CLEARANCE WITH TRAFFIC 1000 FT ABOVE MAINTAINING VISUAL SEPARATION. TCAS RA IS SUBSEQUENTLY RECEIVED AND FLT CREW COMPLIES.

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WHILE IN LEVEL FLT AT 14000 FT MSL; WE NOTICED A TCAS TARGET 1000 FT ABOVE; SLIGHTLY BEHIND US; AND TO THE L. ATC QUERIED THE OTHER ACFT IF THEY HAD US IN SIGHT (VISUALLY). THEY RESPONDED 'YES.' ATC THEN ASKED THE OTHER ACFT IF HE (ATC) ISSUED A CLB CLRNC TO US; WOULD THEY (OTHER ACFT) BE ABLE TO MAINTAIN VISUAL SEPARATION FROM US. THEY RESPONDED 'YES' AND THAT THEY WOULD MAINTAIN VISUAL SEPARATION. ATC THEN ISSUED A CLB CLRNC (I DO NOT RECALL THE NEWLY CLRED ALT -- IT MAY HAVE BEEN 'CLB TO AND MAINTAIN FL230') AND INFORMED US THAT THE TFC WOULD MAINTAIN VISUAL SEPARATION FROM US DURING OUR CLB THROUGH THEIR ALT. WE RELUCTANTLY ACCEPTED THE CLB CLRNC AND I BRIEFED THE PLT MONITORING (SIC) THAT I WOULD RESPOND TO ANY POSSIBLE TCAS RA'S. HE AGREED AND WE BEGAN OUR CLB; AS CLRED. SHORTLY AFTER BEGINNING THE CLB AND APPROX 500 FT BELOW THE TFC; WE RECEIVED A TCAS RA TO 'MONITOR VERT SPD' AND THE VSI DISPLAYED A GREEN RANGE AROUND 0 FPM. WE COMPLIED WITH THE TCAS RA; ADVISED ATC THAT WE WERE FOLLOWING THE RA; AND WHEN CLR OF CONFLICT; ALSO ADVISED THAT WE WOULD RESUME THE CLB. DURING THIS TIME; THE OTHER ACFT (REGIONAL JET) HAD MOVED FROM SLIGHTLY L AND BEHIND US (ACCORDING TO OUR TCAS DISPLAY) TO AHEAD AND R OF US. THE OTHER ACFT DID NOT MAKE ANY OTHER COMS AND AFTER THE EVENT; NOTHING ELSE WAS SAID BY ANYONE. CHAIN OF EVENTS/HUMAN PERFORMANCE CONSIDERATIONS: I BELIEVE THAT POSSIBLE CONTRIBUTING FACTORS IN THIS EVENT INCLUDE: THE OTHER ACFT EITHER NOT UNDERSTANDING THE ACTION NECESSARY TO SEE AND AVOID US AND/OR NOT TAKING THE APPROPRIATE ACTION AS SUCH. ALSO; IN CONSIDERATION OF POSSIBLE FUTURE EVENTS; I WOULD LIKELY NOT ACCEPT A CLRNC LIKE THIS AND INFORM ATC THAT I WOULD PREFER TO WAIT UNTIL ATC SEPARATION CAN BE PROVIDED.