A CHALLENGER 600 FLC; ON A VISUAL APCH TO LUK; FLEW THROUGH 22OH AIRSPACE WITHOUT CLRNC WHILE TRYING TO REMAIN CLR OF CLOUDS.

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WE WERE DSNDING VISUALLY FOR A LNDG AT LUK ARPT. A LARGE AREA OF HVY RAIN AND TSTMS HAD PREVIOUSLY MOVED ACROSS THE ARPT AND THE WX SEEMED TO BE CLRING RAPIDLY BEHIND IT. WE CONTINUED DSCNT AND AS WE CAME WITHIN 5-6 MI OF THE ARPT AN AREA OF LOW STRATUS CLOUDS FORMED BTWN US AND THE FIELD PREVENTING US FROM SEEING THE FIELD. WE BEGAN A R TURN IN AN ATTEMPT TO MAINTAIN A VISUAL WITH THE RWY AND CONTINUED DSCNT. TURNING FURTHER TO THE R WE PICKED UP THE ARPT VISUALLY AT WHICH TIME THE TWR CTLR CALLED US TELLING US WE WERE TOO LOW AND IN THE AIRSPACE OF AN ADJACENT FIELD. AT OUR 1 O'CLOCK POS AND 2 MI WAS BLUE ASH ARPT; WHICH NEITHER OF US KNEW ABOUT. A NORMAL APCH AND LNDG WERE EXECUTED FROM THAT POINT. NO CONTACT WAS EVER ATTEMPTED WITH THE OTHER CTL TWR AND; TO OUR KNOWLEDGE; NO TFC CONFLICTS EXISTED. I PERSONALLY PLACED AN UNSOLICITED CALL TO THE LUK TWR TO EXPLAIN WHY WE FLEW THE PROC. IT WAS STRESSED THAT WE MAINTAINED VFR THE ENTIRE TIME AND SHOULD HAVE ALERTED THEM THAT WE LOST LINE OF SIGHT CONTACT WITH THE ARPT. AS CREW MEMBERS WE WERE BOTH AT THE TIME NEVER IN DOUBT OF ACQUIRING VISUAL WITH THE ARPT BUT MORE CONCERNED ABOUT STAYING WELL CLR OF THE LOWER CLOUD DECK. WE WERE BOTH CONCENTRATING OUR VISION TO THE FORWARD L SIDE OF THE ACFT AND DID NOT NOTICE THE OTHER FIELD OFF OUR R FRONT. CONTRIBUTING FACTORS: THIS WAS THE SECOND LEG OF THE DAY (EWR-LUK). THE FIRST (LEX-EWR) BEGAN AT XA00 THAT SAME MORNING AND WE WERE BOTH LESS THAN WELL RESTED. ALSO WE HAD JUST SPENT 1/2 HR NEGOTIATING OUR WAY THROUGH A VERY ACTIVE FRONTAL ZONE. LOOKING BACK; I WOULD SAY FROM NOW ON I SHOULD IMMEDIATELY RELAY TO THE CTLR ANYTHING NONSTANDARD. THEY COULD HAVE PROVIDED US WITH VECTORS OR THE ABILITY TO ENTER THE OTHER ARPT'S AIRSPACE.