A JS41 CREW MISINTERPED DEP CLRNC AND MAINTAINED RWY HDG.

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ON THE GND AT UNV (STATE COLLEGE; PA); THE FO OBTAINED OUR CLRNC FROM CTR WHILE I MONITORED UNICOM. HE BRIEFED THE CLRNC AS FOLLOWS FOR DEP: 'RWY HDG; 4000 FT.' WE DEPARTED AND CONTINUED CLB UP TO 9000 FT ON RWY HDG OF 240 DEGS. DURING THE CLB WE MADE RADIO CONTACT WITH CTR ON 2-3 OCCASIONS. EACH TIME; I ENDED MY RESPONSE WITH 'RWY HDG' (TO BRING TO CTR'S ATTN THAT WE WERE ON RWY HDG STILL). AT APPROX 5 MINS AFTER TKOF; CTR ADVISED THAT WE WERE TO PROCEED DIRECT TO HYPER INTXN AND THAT WE WERE NEVER CLRED TO FLY RWY HDG. HENCE; OUR RTE OF FLT TOOK US INTO ANOTHER SECTOR'S AIRSPACE. THE MISUNDERSTANDING OF THE INITIAL CLRNC BY THE FO WAS THE BEGINNING OF THE PROB. THE SUBSEQUENT 2 OR 3 RADIO XMISSIONS WITH CTR AFTER DEP COMPOUNDED THE PROB. CTR WAS WORKING AT LEAST 2 FREQS AND HAD DIFFICULTY AFFIRMING OUR RESPONSE THAT WE WERE CLBING TO 9000 FT; DUE TO FREQ CONGESTION. AFTER EVERY RESPONSE; I ENDED THEM WITH 'RWY HDG' (IN ORDER TO STATE OUR FLT TRACK AND RECONFIRM OUR CLRNC). WITHOUT HEARING A CORRECTIVE CLRNC FROM CTR; WE CONTINUED ON RWY HDG. AS CAPT; I COULD HAVE BEEN MORE ASSERTIVE WITH CTR REGARDING OUR CLRNC OF RWY HDG. THE CLRNC RELAYED TO ME FROM THE FO SEEMED A LITTLE OUT OF THE ORDINARY; HOWEVER; OVER THE SEQUENCE OF EVENTS THAT TRANSPIRED; THERE WAS NO REASON TO QUESTION IT.