AN ACR LGT TURNED AND CLBED IN RESPONSE TO A TCASII COMMAND. THE RPTING ACFT WAS IN IMC.

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I WAS THE FO FLYING THE ACFT. BECAUSE OF THE TSTMS AND TURB WE HAD STOPPED OUR CLB AT 2500 FT MSL. DEP CTL WAS ADVISED AND WE WERE TOLD 'ROGER; PLT'S DISCRETION TO 10000 FT; DIRECT ORL WHEN ABLE.' I HAD MY FULL ATTN FOCUSED ON FLYING THE ACFT AND LOOKING OUTSIDE FOR A HOLE TO GET ABOVE THE SHIELD CLOUDS. WHEN DEP ADVISED OF THE TFC AT 12 O'CLOCK; 3400 FT; UNVERIFIED; THE CAPT RESPONDED HE HAD THE TFC ON TCASII BUT BECAUSE OF THE WX (IMC) WE DID NOT HAVE A VISUAL. AT THE SAME TIME; I SAW A HOLE AT OUR 2 O'CLOCK POS AND ADVISED THE CAPT I WAS CONTINUING MY CLB TO 10000 FT. I CALLED FOR CLB PWR; INCREASED THE PWR; ROLLED THE ACFT INTO A 30 DEG R BANKING TURN AND BEGAN A FAIRLY AGGRESSIVE CLB TO GET ABOVE THE WX. THE CAPT; IN AN URGENT VOICE; SUDDENLY SAID 'HARD R!' I IMMEDIATELY ROLLED INTO 40 DEG BANK AND INCREASED MY CLB. SOON AFTER (30 SECONDS) WE BROKE OUT OF THE WX AND THE CAPT ADVISED ME WE ALMOST HIT AN ACFT. I NEVER SAW THE ACFT NOR DID WE RECEIVE A TA FROM THE TCASII (THE TCASII WAS IN TA/RA MODE). THE CAPT ADVISED DEP OF WHAT HAPPENED. 5 MINS LATER; IFR TFC PASSED 1200 FT BELOW US AND WE DID GET A TA 'TFC; TFC' (THE TCASII ALSO TESTED NORMALLY). SUPPLEMENTAL INFORMATION FROM ACN 249249: CAPT'S IVSI DISPLAYED TFC PLUS 300 FT VERY CLOSE TO OUR ACFT. WE WERE IMC AND COULD NOT GET VISUAL CONTACT. ALMOST IMMEDIATELY THE TFC SYMBOL WENT OFF OUR TCASII DISPLAYS. WE RECEIVED NO ASSOCIATED VERBAL TA'S OR RA'S.