B737 CREW MISSES XING ALT RESTR DSNDING ON WRAPS 5 ARR.

Narrative

CRUISING AT FL350 WE WERE GIVEN A XING RESTR TO CROSS TURLO AT FL240. MY FO READ BACK THE CLRNC CORRECTLY; BUT FOR SOME UNKNOWN REASON; I INTERPED THE CLRNC AS PLT'S DISCRETION TO FL240. AT THAT POINT THERE WAS CLRLY A COM BREAKDOWN BTWN ME AND MY FO FOR HE DID NOT CORRECT ME IN MY READBACK TO HIM. PERHAPS BECAUSE HE DIDN'T CLRLY HEAR MY RESPONSE AND ASSUMED I HEARD THE CORRECT CLRNC. AT A POINT BEFORE REACHING TURLO INTXN THE CTR CTLR ASKED THAT WE START OUR DSCNT. I INITIATED A 1000 FPM DSCNT AND MY FO WENT OFF THE #1 RADIO (ATC) TO GET THE ARR ATIS. AGAIN STILL BELIEVING I HAD DISCRETION TO FL240; I CONTINUED MY DSCNT AT 1000 FPM. A LITTLE WHILE LATER; MY FO WAS BACK ON #1 RADIO AND THEN WE RECEIVED THE CALL ASKING IF WE WERE GOING TO MAKE TURLO AT FL240. A QUICK XCHK SHOWED WE WERE ALREADY PAST TURLO AT AN ALT OF FL315. WE WERE THEN GIVEN VECTORS OFF THE ARR TO AVOID TFC INTO THE OAKLAND ARPT. ONLY THEN DID I REALIZE I MADE A MISTAKE IN THE CLRNC RECEIVED AT CRUISE. MY FO WAS NOT ABLE TO BACK ME UP BECAUSE HE WAS DISTR WITH GETTING ATIS DURING MY DSCNT. THIS MISTAKE WAS PLT ERROR. THE 2 OF US NOT CLRLY COMMUNICATING ALT XING RESTRS. AN ERROR BOTH OF US NEED TO PREVENT FROM HAPPENING AGAIN.