CAPT OF AN MLG TAXIED ACROSS A TXWY AND A RWY CONTRARY TO THE TWR'S INSTRUCTIONS AFTER TURNING OFF THE RWY AFTER LNDG.

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I WAS THE FO ON (ACR) AIRLINES FLT FROM NEWARK TO ST LOUIS. THIS WAS THE FIRST LEG OF A MULTIPLE DAY TRIP. THE CAPT AND FO DID NOT KNOW EACH OTHER AND HAD NEVER FLOWN TOGETHER PRIOR TO THIS TRIP. THE CAPT IS ASSIGNED TO THE TRAINING DEPT AND WAS ASSIGNED TO THIS TRIP TO FULFILL HIS REQUIREMENT TO FLY 2 DAYS PER MONTH ON THE LINE. THE FO HAD APPROX 80 HRS IN THE R SEAT AND HAD RECENTLY UPGRADED FROM SO (FE). AT APPROX XX00 WE LANDED ON RWY 30R AT ST LOUIS LAMBERT FIELD AND TOOK THE HIGH SPD EXIT AT INTXN 'G.' SHORTLY AFTER EXITING THE RWY TWR CALLED AND GAVE CLRNC TO 'HOLD SHORT AT TXWY P; CONTACT GND POINT NINER.' AT ABOUT THIS SAME MOMENT WE WERE APCHING RWY 30L AND HAD UNKNOWINGLY ALREADY PASSED TXWY P WHICH IS THE PARALLEL TXWY BTWN 30L AND RWY 30R. AS WE CAME TO RWY 30L THE CAPT INQUIRED 'ARE WE CLR TO CROSS?' I RESPONDED 'I'M NOT SURE -- HOLD HERE WHILE I CHK WITH THE TWR.' I CALLED THE TWR AND ASKED 'IS ACR CLR TO CROSS RWY 30L?' TWR DID NOT RESPOND TO THIS CALL. AS WE WAITED FOR THE RESPONSE FROM TWR I OBSERVED AN ACFT IN POS FOR TKOF ON RWY 30L AND THERE WAS ANOTHER ACFT XING RWY 30L AT INTXN R WHICH WAS BTWN US AND THE ACFT POSITIONED FOR TKOF. BEFORE I WAS ABLE TO MAKE MY SECOND CALL TO TWR THE CAPT ANNOUNCED 'SINCE HE'S XING (THE OTHER ACFT) I ASSUME WE ARE OK TO CROSS.' -- HE THEN PROCEEDED TO CROSS RWY 30L. I WAS VERY SURPRISED THAT HE HAD MADE THIS ASSUMPTION BEFORE I HAD A CHANCE TO CLARIFY OUR CLRNC. ONCE WE CROSSED THE RWY AND HAD CONTACTED GND CTL WE WERE INSTRUCTED TO CONTACT THE TWR VIA THE TELEPHONE. CONTRIBUTING FACTORS: I FEEL THERE WERE SEVERAL THINGS THAT CONTRIBUTED TO THE CONFUSION WHICH CAUSED THE CAPT TO 'ASSUME' WE WERE CLRED TO CROSS. WHEN WE WERE ISSUED THE CLRNC TO HOLD AT TXWY P WE WERE AT OR LIKELY PAST TXWY P. THERE IS A HOLDING AREA N ON TXWY P AT TXWY G THAT MAKES IT HARD TO IDENT TXWY P. NEITHER THE CAPT OR I RECALL SEEING A TXWY P IDENTIFIER AFTER RECEIVING THE CLRNC. I ALSO FEEL THAT THE OTHER ACFT SEEN XING THE RWY INFLUENCED THE CAPT TO ASSUME THAT HE TOO WAS CLR TO CROSS.