A B737 ON APPROACH TO IAH DEVIATED FROM CHARTED ALTITUDES.

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WE WERE ON THE ILS RWY 12R APCH. THE PATH ON THE ILS RWY 12R WAS IN A CLR AREA; WITH HVY RAIN SHOWERS ON BOTH SIDES OF THE COURSE (ABOUT 3 MI AWAY; L AND R SIDES); BUT NOT ON THE COURSE. WE SAW THE HOBBY ARPT AROUND 9-10 MI OUT. CAPT INSISTED HE WANTED THE VISUAL APCH; SINCE WE COULD SEE THE HOU RWY 12R WITH EASE. I QUESTIONED HIM; 'DO YOU 'REALLY' WANT A 'VISUAL'?!' (I WAS NOT TOO COOL WITH THE IDEA; WITH RAIN SHOWERS NEARBY.) CAPT INSISTED; 'YES!' SO I CALLED THE ARPT AND HOUSTON APCH CLRED US FOR THE VISUAL APPROX 2 MI BEFORE ROYCE. I THEN CAUGHT THAT OUR ALT WAS 1800 FT. I CALLED; 'ALT!' CAPT SAID HE 'WAS ON A VISUAL APCH.' I SAID; 'YOU GOT TO MAINTAIN ALT!' WHILE THIS WAS BEING SAID; HE EASED DOWN TO AROUND 1600 FT!' I SAID; 'KEEP YOUR ALT!; CLB!' THEN; ATC CALLED; 'LOW ALT ALERT AND CHK YOUR ALTIMETER.' I ACKNOWLEDGED ATC. THEN I TOLD CAPT (WE WERE PAST ROYCE NOW) 'MAINTAIN YOUR ALT SO YOU CAN INTERCEPT THE GS.' WE HAD A STABILIZED APCH AROUND 1400 FT. I WAS REALLY UPSET. I TALKED TO THE CAPT AFTERWARDS. I TOLD HIM; YOU COULD NOT DSND BELOW 2000 FT ON THE APCH; EVEN ON THE VISUAL APCH; BECAUSE OF THE CLASS B AIRSPACE. HE DIDN'T REALIZE IT AND IMMEDIATELY CALLED ON THE PHONE TO HOU TWR/APCH. TWR TOLD HIM; 'DON'T WORRY ABOUT IT; SINCE YOU WERE ON THE VISUAL; BUT THEY ARE REQUIRED TO WARN US.' KEY THING: CAPT WILL NEVER DO IT AGAIN.