IFR LR35 DEP FROM ZZZ TO HOU EXPERIENCED COM PROBLEMS WITH IFR RELEASE ATTEMPT; DEPARTED VFR WITH IFR CODE; CAUSING ATC CONFUSION.

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OUR MISSION WAS A PAX-CARRYING FLT UNDER FAR PART 135; TO DROP PAX AT ZZZ AND RETURN EMPTY TO HOU. ARR INTO ZZZ WAS UNEVENTFUL; AND AN IFR FLT PLAN WAS FILED TO RETURN TO HOU; EVEN THOUGH THE WX WAS CAVU. ZZZ IS CURRENTLY UNDER CONSTRUCTION (RWY EXPANSION; NEW FACILITIES AND A NEW GCO FOR CLRNC DELIVERY). MY FO ATTEMPTED TO CONTACT HOU CLRNC DELIVERY ON THE GCO; WHICH IS ACTIVATED BY KEYING THE MIKE 4 TIMES AND A REMOTE PHONE CALL IS MADE TO HOU CLRNC DELIVERY. THE GCO WAS MALFUNCTIONING; ATTEMPTING TO PROCESS THE CALL AND THEN RETURNING A 'FAST BUSY' SIGNAL. THE FO THEN CALLED HOU CLRNC DELIVERY ON HIS CELL PHONE AND RECEIVED AN IFR CLRNC TO HOU WITH A VOID TIME OF XA12Z. ZZZ IS JUST ON THE WESTERN EDGE OF THE HOU CLASS B AIRSPACE; AND WAS BUSY WITH SEVERAL VFR ACFT IN THE PATTERN. WE TAXIED OUT TO RWY 18 AND WERE #3 FOR TKOF; MISSING OUR VOID TIME DUE TO THE DELAY. WE THEN ATTEMPTED TO RE-CONTACT HOU CLRNC DELIVERY TO EXTEND OUR IFR CLRNC 4 TIMES. TWICE WE TRIED THE GCO; WHICH CONTINUED TO RETURN A 'FAST BUSY;' SO THE THIRD ATTEMPT WAS VIA TELEPHONE. WE REACHED A CLRNC DELIVERY CTLR WHO ASKED US TO HOLD FOR ABOUT 1 MIN. WE WERE PLACED ON HOLD AND 4 MINS LATER WERE DISCONNECTED; PRESUMABLY A 'DROPPED CALL' ON THE CELL PHONE. WE ATTEMPTED A SECOND PHONE CALL AND RECEIVED THE SAME 'FAST BUSY' WE HEARD ON THE GCO. AT THIS TIME WE PRESUMED THE PHONE CIRCUIT GOING INTO HOU CLRNC DELIVERY WAS MALFUNCTIONING. WE HAD NOW WAITED ON THE TXWY FOR ABOUT 6 MINS; AND WERE HOLDING UP OTHER DEP TFC. I ASKED THE FO TO VERIFY THE LOCATION OF THE CLASS B OUTER RING; AND BRIEFED HIM THAT WE WOULD DEPART ON RWY 18 VFR; CLB DUE S (AWAY FROM THE BRAVO); LEVEL AT 1500 FT AGL AND CONTACT HOU APCH CTL TO WORK OUT OUR CLRNC BACK TO HOU. WE LEFT OUR PREVIOUSLY ASSIGNED XPONDER CODE ACTIVE SO AS TO FLAG THE CTLR AS TO WHO WE WERE; AND MADE THE VFR DEP AS DESCRIBED. AFTER LEVELING AT 1500 FT AGL; WE CONTACTED HOU APCH; WITH THE FOLLOWING VERBIAGE; 'HOUSTON APCH; THIS IS LEARJET X.' THE CTLR (WHO WAS QUITE BUSY) IMMEDIATELY REPLIED WITH; 'LEARJET X RADAR CONTACT; CLB AND MAINTAIN 3000 FT; L TURN TO 090 DEGS; RADAR VECTORS TO HOBBY.' WE ASSUMED HE HAD EITHER EXTENDED OUR CLRNC VOID TIME OR REACTIVATED OUR IFR STATUS; SO WE ACKNOWLEDGED HIS INSTRUCTIONS AND COMPLIED. AFTER LNDG AT HOU; WE WERE ASKED BY GND CTL TO GIVE THE TRACON SUPVR A PHONE CALL TO DISCUSS A POSSIBLE PLTDEV. I SPOKE WITH THE SUPVR WHO WAS VERY PLEASANT; BUT TOLD US THAT WE HAD BEEN GIVEN A VOT OF XA12; AND THAT WE DEPARTED UNDER IFR AT XA20. I RELAYED TO HIM THE ENTIRE STORY OF OUR ATTEMPTING TO RECONTACT CLRNC DELIVERY VIA TELEPHONE AND RADIO; AND THAT WE HAD DEPARTED UNDER VFR AND INTENTIONALLY REMAINED ON AN ALT AND HDG THAT KEPT US CLR OF THE CLASS B UNTIL WE SPOKE TO A CTLR FROM HOUSTON WHO GAVE US A CLRNC; WHICH WE FOLLOWED. SUPVR ASKED IF WE HAD STATED TO THE CTLR THAT WE WERE IN FACT VFR; AND IF WE HAD ATTEMPTED TO CLARIFY OUR FLT STATUS. I TOLD HIM NO; THAT WE HAD NOT; BECAUSE IT IS MY UNDERSTANDING THAT IF WE IN FACT DEPART AFTER A CLRNC VOID TIME THAT WE HAVE NO IFR CLRNC; AND THAT THE OP MUST IN FACT BE UNDER VFR. FROM THE PERSPECTIVE OF THE FLT CREW; IT MADE NO OPERATIONAL DIFFERENCE WHETHER THE CTLR GAVE US A VFR CLRNC OR AN IFR CLRNC; AS LONG AS WE WERE IN FACT CLRED INTO THE BRAVO AND UNDER RADAR CONTACT. I ASKED THE SUPVR IF HE COULD SUGGEST A POLICY CHANGE AT OUR COMPANY TO PREVENT HAVING SUCH MISUNDERSTANDINGS IN THE FUTURE; AND HE ADVISED THAT IT WOULD IN FACT HELP IF WE REITERATED TO OUR PLTS THAT IT IS IMPORTANT THAT THERE IS A FULL UNDERSTANDING BTWN THE CREW AND THE CTLR OF THE FLT'S STATUS; WHETHER VFR OR IFR. I TOLD HIM I WOULD FILE AN INTERNAL INCIDENT RPT WITH OUR COMPANY'S DIRECTOR OF SAFETY WHO WOULD THEN BRIEF OUR PLTS AT THE NEXT SAFETY MEETING; AND THE SUPVR INDICATED HE WOULD BRIEF THE CTLR ON THE MISUNDERSTANDING AND 'MARK IT DOWN AS A LEARNING EVENT.' UPON REFLECTION OF THE INCIDENT; IT WOULD OBVIOUSLY BE MOST HELPFUL IF THE GCO AND TELEPHONE LINES INTOHOUSTON CLRNC ARE OPERATIONAL. FURTHER; WHILE WE AS A PART 135 OPERATOR DO HAVE APPROVAL TO DEPART VFR AND PICK UP AN IFR CLRNC AIRBORNE; WE ARE PUBLISHING A NEW SOP FOR FLT CREW MEMBERS ON THE NEED TO BE ABSOLUTELY CERTAIN OF THE STATUS OF THE FLT; AND TO CLARIFY THAT STATUS WITH ATC AFTER DEP IF NECESSARY. FURTHER; ALL VFR DEPS MUST NOW BE MADE WITH A XPONDER CODE OF 1200 UNLESS MITIGATING CIRCUMSTANCES EXIST SUCH AS VFR FLT WITHIN A TFR; OR A VFR CODE IS SPECIFICALLY ISSUED BY ATC.