LEAR 25 FLC CLBED ABOVE THEIR ASSIGNED VFR ALT DUE TO MISUNDERSTANDING OF A CLRNC TO ANOTHER ACFT.

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WE WERE IN A LEAR 25; CRUISING TO W-291. WE WERE TALKING TO SOCAL CTL W OF SLI AT ABOUT 10 MI. SOCAL HAD ASKED US TO MAINTAIN AT OR BELOW 11500 FT. I THEN HEARD A XMISSION THAT SOUNDED LIKE EXPEDITE CLB TO 15500 FT. AS PF; I INITIATED A CLB TO 15500 FT AND THE PNF WAS LOOKING OUTSIDE FOR OTHER TFC. THE RADIO SYS IN THE LEAR IS SET UP WITH A HOT MIKE SYS; BUT BECAUSE OF DISTORTION AND STATIC; THE PNF TURNED OFF THE HOT MIKE AND I DID NOT HEAR HIS XMISSIONS TO ATC. SINCE WE HAD REQUESTED 15500 FT; I ASSUMED WE HAD BEEN ASKED TO CLB TO 15500 FT AS SOON AS POSSIBLE. I INITIATED A CLB AND AS WE NEARED 15000 FT WE SIGHTED A JETLINER (I THINK A B737) DSNDING AT ABOUT OUR 2-3 O'CLOCK POS. I BEGAN A GENTLE L TURN AND NOTICED THE AIRLINER WAS IN A GENTLE L TURN. IN MY ESTIMATION; WE NEVER CAME CLOSER THAN 1000 FT BUT WE MAY HAVE SET OFF HIS TCASII. THE PNF ADVISED ME THAT ATC HAD SAID NOT TO CLB ABOVE 15000 FT. I ATTRIBUTE THE PRIMARY CAUSE OF THIS EVENT TO POOR RADIO EQUIP IN THE LEAR; AND THE INABILITY OF THE PF TO HEAR THE PNF'S COMS. HOWEVER; WE WERE VFR AND SAW THE JETLINER AT LEAST 3 MI FROM US. HOWEVER; BECAUSE ATC SAID THEY HAD NOT CLRED US TO CLB THE PNF (PIC) MADE A CALL TO ATC AFTER THE FLT TO EXPLAIN THE COMS PROB IN THE LEAR AND WHAT OUR ACTIONS HAD BEEN. THE PIC AND I DISCUSSED THE NEED TO STAY ON HOT MIKE AND ALSO TO WRITE UP THE RADIO AND INTERCOM SYS TO BE LOOKED AT WHEN WE RETURNED TO HOME BASE. SUPPLEMENTAL INFO FROM ACN 521462: THE FLT WAS A PRACTICE FLT FOR A FUTURE PHOTO MISSION. THE AIRPLANE DEPARTED ON A VFR DEP OUT OF CLASS C AIRSPACE TO THE SE. SOCAL CLRED US DIRECT TO SEAL BEACH. AT THIS TIME THE R SEAT PLT BECAME OCCUPIED SETTING IN COORDINATES IN THE GPS FOR A TARGET WAYPOINT IN WARNING AREA 291. AT THIS TIME THE FLC HEARD A XMISSION WHICH INCLUDED '15000 FT.' THE FLC DID NOT ASK FOR A CLARIFICATION. THE FLC ASSUMED THAT WE WERE NOW FREE TO CLB TO VFR ABOVE 11500 FT. NO RPT THAT THE CLB WAS BEING MADE WAS XMITTED. THE AIRPLANE CLBED AND LEVELED OFF AT 15500 FT. SOCAL CALLED AND REQUESTED THE AIRPLANE'S ALT. DURING THE ENSUING COMS EXCHANGE SOCAL CALLED OUT CONFLICTING TFC AND REQUESTED THAT WE DSND IMMEDIATELY. THE B737 MADE A DSNDING L TURN AND PASSED APPROX 1000 FT BEHIND AND 500 FT BELOW. UPON COMPLETION OF THE FLT A TELEPHONE CALL WAS MADE TO THE TRACON SUPVR. A THOROUGH DISCUSSION OF EVENTS TOOK PLACE. THE SUPVR SAID THAT NO VIOLATION WOULD BE FILED BY THE TRACON SINCE WE WERE OPERATING VFR IN A SEE AND BE SEEN ENVIRONMENT.