FLC OF AN LTT JET AMB OVERSHOT CLB ALT ASSIGNMENT DUE TO THE FO NOT INFORMING THE FLYING CAPT.

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ACFT JUST TOOK OFF FROM FXE WITH A CLRNC OF RADAR VECTORS BIMINI; AS FILED. WE WERE CLRED TO 16000 FT AND AS WE PASSED THROUGH 10000 FT THE CABIN ALT WARNING SOUNDED SIMULTANEOUSLY WITH BOTH ENG BLEEDS REVERTING TO EMER BLEED. THIS FLOODED THE CABIN WITH SMOKEY HOT BLEED AIR ALONG WITH MUCH NOISE OF RUSHING AIR. JUST SECONDS INTO THIS; ATC XMITTED SOMETHING AND MY COPLT RESPONDED. I CONTINUED TO DEAL WITH THE PRESSURIZATION PROB. I THEN HEARD ATC SAY TO JUST MAINTAIN 13000 FT. I HEARD THIS AT 12500 FT INDICATED. THE PREVIOUS XMISSION THE COPLT THEN TOLD ME WAS AN AMENDMENT OF OUR PREVIOUS CLRNC TO 16000 FT TO 11000 FT. I NEVER HEARD THE AMENDMENT DUE TO MY PREOCCUPATION WITH SMOKE AND NOISE FROM THE EMER BLEED AIR. MY COPLT DID BUT DID NOT PUT 11000 FT IN THE WINDOW NOR SEE TO IT I HEARD THE AMENDMENT. AS IT TURNS OUT; ON HER PREFLT THE COPLT DID NOT TURN THE ENG BLEEDS ON THUS WE WERE UNPRESSURIZED. SHE WAS TOO EXCITED TO MONITOR THE PLANE AND INFORM ME OF THE AMENDED ALT CLRNC. THIS COPLT IS BRAND NEW AND HAS LITTLE EXPERIENCE. SHE DID NOT PERFORM A PROPER PREFLT AND DID NOT RELAY THE ATC INSTRUCTIONS TO THE PF. THE WHOLE INCIDENT CAN BE ATTRIBUTED TO HER INEXPERIENCE. THESE CHEAP; WILLING; INEXPERIENCED PLTS ARE A DANGEROUS TREND AND SHOULD BE REGULATED OUT OF COMPLEX; HIGH PERFORMANCE TURBO JETS. THESE ACFT ARE DESIGNED FOR 2 PLTS; YET; FOR ALL PRACTICAL PURPOSES; I AM FLYING SINGLE PLT.