ALTDEV ALT UNDERSHOT AS MISSED APCH PROC DELAYED DURING AUTOPLT DISCONNECTION FROM A COUPLED APCH MODE.

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WE WERE JUST CLRED FOR THE APCH AND THE APCH CTLR OR TWR CTLR; I DON'T REMEMBER; TOLD US THE ARPT HAD JUST CONTINUED TO GO DOWN TO 1/2 MI VISIBILITY. WE WERE EXPERIENCING HVY RAIN SO WE ELECTED TO NOT CONTINUE THE APCH AND TOLD THE TWR WE WERE GOING TO CLB BACK UP TO 3000 FT AND OVERFLY OR GIVE US VECTORS FOR ANOTHER APCH. SHE TOLD US TO CLB BACK TO 3000 FT AND EITHER MAINTAIN RWY HDG OR GIVE US A R TURN. I CAN'T REMEMBER. THE AUTOPLT WAS ON AND I HAD SWITCHED THE ALT HOLD OFF BUT THE AUTOPLT HAD CAPTURED THE GS SO IT DIDN'T RELEASE THE GS AND CONTINUED DOWN. BY THE TIME THE FO TURNED OFF THE AUTOPLT THE ACFT HAD COME DOWN TO ALMOST 2500 FT. WE WEREN'T SURE IF WE HAD BROKEN A 300 FT TOLERANCE OR NOT SO ELECTED TO RPT THIS OCCURRENCE. THE CTLR ASKED IF WE HAD ELECTED TO CONTINUE THE APCH SINCE SHE NOTICED WE WERE CONTINUING TO DSND BUT WE TOLD HER WE WERE INDEED GOING AROUND. THE NEXT APCH WAS EVENTLESS AND THE WIND HAD GONE DOWN TO 4 KTS AND GND CONTACT WAS MADE BY 1500 FT AGL. THIS WAS AN IOE FLT; THE FO'S FIRST IOE TRAINING EVENT AND HE WAS THE PF. SUPPLEMENTAL INFO FROM ACN 304330: WHILE BEING VECTORED FOR THE ILS TO RWY 1 AT SDF; ATC NOTIFIED US THAT THE RWY CONDITIONS WERE RVR OF 3000 FT; HVY RAIN AND FOG. WINDS WERE 270 DEGS AT 12 KTS (ALMOST A DIRECT XWIND). THE CAPT ELECTED TO CONTINUE AND SEE IF THE WX CONDITIONS WOULD IMPROVE. AS WE INTERCEPTED THE ILS FINAL; TWR NOTIFIED US THAT 2 PREVIOUS ACFT HAD GONE AROUND AHEAD OF US. UPON HEARING THIS THE CAPT ELECTED TO GAR AND TRY AGAIN. (ALT WAS 2800 FT AND THE FO WAS FLYING A COUPLED ILS APCH.) DURING THE CONFUSION OF THE LAST MIN CHANGE TO DISCONTINUE THE APCH; THE FO LET THE ACFT CONTINUE DOWN THE GS APPROX 200 FT BELOW FINAL APCH FIX ALT. ATC; MEANWHILE; TOLD US TO CLB TO 3000 FT AND TURN EASTERLY. THE FO TRIED TO DISCONTINUE THE APCH BUT THE AUTOPLT WOULD NOT DISCONNECT UNTIL THE ACFT HAD DSNDED TO APPROX 2600 FT TO 2500 FT. I THINK THE COMBINATION OF TASK SATURATION DUE TO THE WX; FLYING THE APCH IN HVY RAIN AND THE LAST MIN CHANGE MADE BY THE CAPT TO DISCONTINUE THE APCH CAUSED THIS MINOR ALTDEV.