B767 PIC CONCERNED WITH FO'S RESPONSE TO TCASII TA-RA WHEN LEVELING AT FL230 WITH TFC PASSING AT FL240.

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ON CLBOUT IN VFR CLR NIGHT CONDITIONS; FO WAS FLYING THE ACFT ON AUTOPLT TO AN ASSIGNED ALT OF FL230. ATC ADVISED OF 1 O'CLOCK TFC LEVEL AT FL240. HIGHER WHEN CLR. I WAS MAKING A PA WHEN AT FL225 WE GOT A TFC ALERT ON TCASII. IT WAS QUICKLY FOLLOWED BY A 'DSND; DSND NOW' RA. THE FO SAW THE TFC AND SAW THAT WE WERE OVER 1000 FT BENEATH THE TFC AND REMAINED ON THE AUTOPLT; BELIEVING THAT IT WAS SAFE TO DO SO. I DIRECTED HIM TWICE TO FOLLOW THE RA AND ALTER OUR CLB. THE TFC PASSED R TO L AND WE GOT A MONITOR VERT SPD; THEN A CLR OF TA AS WE NEARED FL230. WE WERE NEVER CLOSER THAN 1000 FT VERTLY. I SHOULD HAVE TAKEN THE ACFT TO EXECUTE THE PROC MORE QUICKLY; BUT DID NOT ELECT TO GRAB THE CTLS AS I WAS IN THE MIDDLE OF A PA. I DO NOT BELIEVE SAFETY WAS COMPROMISED. SUPPLEMENTAL INFO FROM ACN 501791: THE CTLR CALLED OUT THE POS OF THE ACFT. I RPTED THAT WE HAD IT VISUALLY AND ON TCASII. TCASII INDICATED IT TO BE LEVEL AT FL240. WHEN PASSING FL225; WE RECEIVED A TA WHICH TURNED INTO AN RA ABOUT 200 FT LATER. I ALLOWED THE ACFT TO LEVEL OFF ON ITS OWN AT FL230 AS PER OUR CLRNC.