MISCOM ON ASSIGNED ALT. RPTR FLC READ BACK 13000 FT AND SET IT IN ALT ALERT. ATC INFORMED FLC TO CONTACT THEIR COMPANY AND CAPT WENT OFF ATC FREQ TO CONTACT COMPANY. WHEN RETURNING TO ATC FREQ; THE FLC RECEIVED AN RA ON TCASII; AND REALIZED THEY WERE CLBING INTO THE INTRUDER ACFT. THEN; WHEN CONTACTING DEP CTLR; WERE TOLD THEY WERE SUPPOSED TO MAINTAIN 5000 FT.

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AIRLINE FLT IS A REGULARLY SCHEDULED PAX FLT FROM HONOLULU; OAHU; TO KAHULUI; MAUI. EVERYTHING UP TO THE FOLLOWING EVENT PROCEEDED ROUTINELY. THE FOLLOWING EVENT TOOK PLACE APPROX 13 MI E OF THE HNL VOR WHILE ON V2 AT ALT OF APPROX 6200 FT. UPON CONTACTING HNL DEP CTL OUR FLT WAS ASSIGNED TO INTERCEPT V2 AND TO CLB AND MAINTAIN 13000 FT. WE WERE ALSO INFORMED TO CONTACT OUR COMPANY FOR A MESSAGE. AFTER COMPLETING THE AFTER TKOF CHKLIST THE CAPT CONTACTED OUR COMPANY DISPATCH AND WAS INFORMED OF A TKOF DATA REVISION. HE TOLD DISPATCH TO STANDBY AND RETURNED TO MONITOR ATC XMISSIONS. AFTER INTERCEPTING V2 AND ESTABLISHED IN THE CLB THE CAPT CONTACTED DISPATCH TO COPY THE REVISED TKOF DATA. WHEN THE CAPT TOLD ME 'HE WAS BACK' WE RECEIVED A TA FROM THE TCASII. HE ASKED HNL DEP TO VERIFY OUR ASSIGNED ALT OF 13000 FT AND WE WERE TOLD 'NEGATIVE; MAINTAIN 5000 FT.' AT THIS TIME WE WERE CLBING THROUGH APPROX 6200 FT; SO PWR WAS REDUCED AND WE DSNDED TO 5000 FT. WHILE DSNDING WE RECEIVED AN RA WITH THE AUDIO AND VISUAL INDICATIONS TO DSND. DURING THE DSCNT WE OBTAINED VISUAL CONTACT WITH THE TFC (DC9) AND INFORMED HNL DEP THAT WE HAD THE TFC IN SIGHT. WE WERE ASSIGNED TO MAINTAIN VISUAL SEPARATION WITH THE DC9 AND TO CLB AND MAINTAIN 13000 FT. THE FLT CONTINUED TO KAHULUI; MAUI; WITHOUT ANY OTHER FURTHER INCIDENT. A FEW THINGS MAY HAVE CONTRIBUTED TO THE ABOVE EVENT: A NONSTANDARD ARR RTE INTO HNL USED BY THE DC9 AND THE RADIO XMISSION WITH COMPANY DURING CLB. IF ATC WOULD HAVE POINTED OUT THE DC9 WE MAY HAVE BEEN MORE VIGILANT LOOKING FOR TFC AND THE CAPT MAY HAVE DELAYED HIS DECISION TO CONTACT DISPATCH THE SECOND TIME TO COPY THE REVISED TKOF DATA. ALSO SELCAL SHOULD BE USED TO CONTACT CREWS DURING FLT WITH NON CRITICAL INFO. BELIEVING DISPATCH MAY HAVE INFO OF SOMETHING THAT MAY HAVE THREATENED OUR FLT IT WAS DECIDED TO CONTACT DISPATCH DURING A CRITICAL PHASE OF FLT.