LGT MISINTERPRETS CLRNC; TAXIES ACROSS ACTIVE RWY.

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I WAS THE FO ON FLT DFW TO HOU. AFTER AN UNEVENTFUL LNDG ON RWY 12R AT HOU; WE ROLLED TO THE END AND WERE TOLD TO CONTACT GND ON TXWY M. GND INSTRUCTED US TO PROCEED N ON TXWY M AND HOLD SHORT OF RWY 12L AT TXWY O. I ACKNOWLEDGED THOSE INSTRUCTIONS. WHILE ON TXWY M; AN MLG LANDED ON RWY 12R AND TOOK THE HIGH SPD; TXWY W. WE WERE TOLD TO GIVE WAY TO MLG; AND THEN MLG WAS TOLD TO PROCEED N ON TXWY M AND CROSS RWY 12L AND RWY 4/22 AT TXWY C. MLG ACKNOWLEDGED AND PROCEEDED. AS WE TURNED R ON TXWY O; I TOLD THE CAPT THAT WE HAD NOT BEEN CLRED ACROSS RWY 12L. HE REPLIED THAT WE WERE CLRED ACROSS BEHIND ACFT. I REPLIED THAT I HAD NOT ACKNOWLEDGED THAT CLRNC. BY THIS TIME WE HAD CROSSED ONTO RWY 12L; TWR IMMEDIATELY CALLED US TO SAY THAT WE CROSSED ONTO AN ACTIVE RWY. OUR CAPT REPLIED TO GND THAT LGT WAS CLRED ACROSS RWY 12L AND 4/22. TWR REPLIED THAT CLRNC WAS FOR MLG AND THAT AN SMA HAD TO ABORT HIS TKOF. WE WERE THEN CLRED TO OUR GATE. CONTRIBUTING FACTORS: 1) WE WERE TOLD TO HOLD SHORT OF RWY 12L WHILE ON TXWY M; BUT MLG WAS CLRED ACROSS RWY 12L IN FRONT OF US; EVEN THOUGH THEY HAD LANDED AFTER US. 2) THE GND CTLR TOLD US TO GIVE WAY TO MLG AND THEN PROCEEDED WITH MLG CLRNC; WITHOUT GETTING AN ACKNOWLEDGEMENT FROM US TO GIVE WAY. 3) WE WERE SWITCHED TO GND FREQ AFTER LNDG; EVEN THOUGH WE WOULD HAVE TO CROSS AN ACTIVE RWY. THIS DID NOT ALLOW US TO MONITOR TWR FREQ AND CONFLICTS THAT MIGHT ARISE; I.E.; THE SMA GIVEN TKOF CLRNC ON RWY 12 AFTER MLG AND BEFORE US. HUMAN PERFORMANCE CONSIDERATIONS: 1) NOT STOPPING TO CONFIRM A CLRNC. 2) KEEPING ACFT ON TWR FREQ UNTIL ACROSS ALL ACTIVE RWYS (AS IS COMMON PRACTICE AT MOST MAJOR ARPTS). 3) MAKING SURE ALL CLRNCS GIVEN ARE GIVEN TIME TO BE ACKNOWLEDGED AND ARE! AT NO TIME WAS THE SMA EVER IN DANGER OF STRIKING OUR AIRPLANE.