MLG OVERSHOT ALT ON CLIMBOUT AND HAD LESS THAN STANDARD SEPARATION WITH OPPOSITE DIRECTION TRAFFIC. NO TRAFFIC ADVISORY GIVEN; MISINTERP ALT ASSIGNMENT.

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WE DEPARTED DFW FOR A FLT TO SNA. OUR CLRNC WITH DEP WAS TO FLY THE WORTH 4 DEP; CORONA TRANSITION. DEP CTL ORIGINALLY CLRED US ON THE SID UP TO 17000'; PARALLELING ANOTHER AIRLINER ON THE SAME SIDE; AMARILLO TRANSITION. DEP CTL THEN SWITCHED US OVER TO CENTER WHO CLRED US UP TO 33000' ON COURSE. PASSING THROUGH APPROX 23500' CENTER THEN SWITCHED US OVER TO ANOTHER CENTER FREQ. JUST AS I WAS ABOUT TO CALL THAT FREQ AND PASSING THROUGH 24700' THE CAPT SAW A TWIN ENG ACFT PASS BELOW US AND TO OUR LEFT. HE ESTIMATED THE VERT SEP AS 700'; HORIZ SEP AS 500-1000'. I THEN CALLED CENTER AND RPTED CLBING TO FL330. CENTER RESPONDED THAT THERE WAS AN ACFT AT OUR ALT IN OUR VICINITY. THE CAPT REPLIED 'WE JUST WENT BY HIM.' CENTER THEN TOLD US TO EXPEDITE THROUGH FL250; WHICH WE DID. NO FURTHER CLRNCS WERE ISSUED. THE CAPT OBTAINED A TELEPHONE NUMBER TO CALL WHEN WE ARRIVED IN ORANGE COUNTY. SUBSEQUENTLY PASSING THROUGH FL310 CENTER TOLD US TO DSND AND MAINTAIN FL310. WE REMAINED THERE FOR QUITE A WHILE AND ONE CENTER SECTOR CHANGE. WE THEN REQUESTED AND RECEIVED A CLRNC TO FL350; OUR FILED CRUISING ALT. IN THIS INSTANCE IT WAS CLEARLY A COM ERROR. THE READBACK TO CENTER WAS FOR FL330 AND WAS NOT CHALLENGED. NO TFC WAS ISSUED TO US EVEN THOUGHT IT WAS OPP DIRECTION AND SUPPOSED TO BE 1000' ABOVE US. THIS MAY HAVE PROVIDED US WITH A CLUE WITH WHICH TO CHALLENGE OUR CLRNC. SUPPLEMENTAL INFO FROM ACN 95182: AFTER SWITCHING TO CENTER FREQ WE WERE CLRED TO WHAT THE F/O AND I BOTH HEARD TO BE FL330. F/O READ BACK FL330. I CONTINUED CLBING. AFTER PASSING FL230 (RATE OF CLB APPROX 2500 FPM) CENTER CLRED US TO SWITCH FREQS AND CLOSED WITH 'SORRY ABOUT THAT.' (THAT PHRASE ONLY MADE SENSE LATER.) PASSING 24700' I WAS SHOCKED TO SEE A TWIN ENG ACFT AT OUR 9 O'CLOCK POS APPROX 700' LOWER AND ABOUT 500-1000' HORIZ SEP. AT THIS SAME MOMENT THE F/O WAS CHKING IN WITH CENTER WITH; 'CLBING TO FL330.' CENTER RESPONDED WITH; 'YOU WERE SUPPOSED TO LEVEL AT FL230; TFC AT FL240; EXPEDITE THROUGH FL250.' THE F/O REPLIED; 'WE WERE CLRED TO FL330;' AND I REPLIED; 'THE TFC ALREADY WENT BY.' THE CTLR REPEATED; 'EXPEDITE THROUGH 250;' AND ASKED IF WE WISHED TO FILE A NEAR MISS RPT. I REPLIED; 'I'LL THINK ABOUT IT.' AS WE PASSED THROUGH 31000' THE CTLR INSTRUCTED US TO MAINTAIN FL310. AFTER LEVELING AT FL310 I REQUESTED AND RECEIVED A TELEPHONE NUMBER FOR WHICH TO CALL FT WORTH CENTER. IN RETROSPECT; I SURMISED THAT THE CTLR; WHO CLRED US TO CLB; IN HER HASTE TO CLR US ABOVE WHAT SHE UNDERSTOOD OUR CLRNC LIMIT TO BE; FAILED TO SEE US PASSING THROUGH FL230 OR TO ISSUE A TFC ADVISORY. ALTHOUGH INFORMED BY FT WORTH CENTER THAT THEIR TAPES RECORDED THE CTLR ISSUING A CLRNC TO FL230 AND OUR READBACK ACKNOWLEDGING FL230; I HAVE SOME GRAVE DOUBTS AS BOTH THE F/O AND I WERE CERTAIN WE HAD HEARD AND READ BACK FL330. I AM NOT NEARLY AS CONCERNED OVER PLACING THE BLAME AS I AM ABOUT ENSURING THAT THIS INCIDENT NEVER AGAIN OCCURS. I WOULD SUGGEST THAT CENTER SECTORS BE GIVEN MORE OVERLAP WHERE POTENTIAL TFC CONFLICT EXISTS. OR; PERHAPS THAT CTLRS NOT BE SO EAGER TO DO ME ANY FAVORS. FOR MY PART; I WILL INTENSIFY MY EFFORTS TO HEAR AND UNDERSTAND EVERY COM TO AND FROM MY ACFT WHETHER OR NOT I AM HANDLING THE RADIOS.