CAPT OF A B727 OVERSHOT ASSIGNED ALT AFTER CORRECTING BACK FROM FOLLOWING A TCASII DIRECTED DSCNT.

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FLT FROM COS TO MEM; GIVEN CLRNC DIRECT GCK WITH CLB TO FL230 FROM ZDV. IT WAS THE CAPT'S LEG AS HE WAS STILL ON HIGH MINIMUMS. ZDV AMENDED OUR CLB TO FL200 FOR TFC. THE CAPT HAD THE AUTOPLT ENGAGED AND AS WE APCHED FL200 I COULD SEE THE CONFLICTING TFC; OPPOSITE DIRECTION AT ABOUT 11 O'CLOCK POS WITH ITS LNDG LIGHT ON. ATC POINTED OUT THE TFC AND I RESPONDED WE HAD THE TFC IN SIGHT. AT THIS TIME THE TCASII ISSUED A TA; AND SECONDS LATER THE TCASII ISSUED COMMANDS TO 'DSND; DSND' AT WHICH TIME THE CAPT DISENGAGED THE AUTOPLT AND INITIATED A DSCNT. I ADVISED ATC OF THE RA AND TOLD HIM WE WERE DSNDING. AT THIS TIME THE TCASII ISSUED 'MONITOR DSCNT' COMMAND. WE HAD DSNDED APPROX 300 FT. I HAD BEEN WATCHING THE TFC IN THE WINDOW AND JUST AFTER THE 'MONITOR DSCNT' COMMAND; I NOTICED THE CAPT HAD BEGUN A CLB AND WE WERE ABOUT TO CLB THROUGH FL200. I PLACED A SMALL AMOUNT OF FORWARD PRESSURE ON THE CTL COLUMN AND RESPONDED 'DON'T CLB; DON'T CLB.' THE CAPT RE-ENGAGED THE AUTOPLT AND BROUGHT THE ACFT BACK TO FL200 AFTER BALLOONING APPROX 200-300 FT ABOVE FL200 AND AT ABOUT THE TIME THE TCASII ISSUED 'CLR OF CONFLICT.' SHORTLY THEREAFTER; CTR ASKED FOR OUR ACCOUNT OF THE EVENT. I RESPONDED THAT WE HAD THE RA AND DSNDED. THE CTLR ASKED US TO VERIFY THE ALT WE WERE CLRED TO AND I RESPONDED FL200; AND THEN AFTER A FEW MOMENTS ASKED WHY; IF WE HAD A DSCNT RA; HAD WE CLBED 300 FT ABOVE FL200; FOR THAT WAS WHAT THEIR EQUIP HAD SHOWN. THE CAPT AND SO TOLD ME THAT THEY HAD HEARD THE TCASII ISSUE CLB INSTRUCTIONS. I; HOWEVER; DON'T RECALL THAT AND TOLD ATC THE SAME. I FEEL MANY FACTORS CONTRIBUTED TO THIS EVENT: 1) HIGH MINIMUMS CAPT. 2) INADEQUATE TRAINING ON NEW TCASII EQUIP. 3) BACK SIDE OF THE CLOCK FLYING. 4) CAPT ATTEMPTING TO DIVIDE HIS ATTN BTWN WATCHING THE TFC AND FLYING THE ACFT.