The thread title reads "type heavy rain" as if there would be some kind of initiative on your part in doing so, but there is a little surprise: i've done the typing for you.
Disclaimer: Heavy Rain is a work of fiction. Characters are typed to the extent they can be typed at all only.
Video with Madison first and Norman Jayden second:
Video with Scott Shelby and Lauren (interesting from 4:20):
Jayden, Blake and some lunatic ENFj:
Ethan Mars and some INTj psychologist, also with Shaun Mars @ 5:00:
Ethan Mars: INFj - very sensitive, capable of going through anything to save his sons. Lives by a clear schedule and is a very caring father.
Scott Shelby: INTp - a calm and controlled guy who is not afraid of getting his hands dirty. Has extreme planning skills while also showing a compassionate side. Says about himself "tact isn't exactly my strong suit".
Madison: ESTj - physically confident, rides a motorcycle. Fits the image of a tough woman while not being violent in any kind of initiative taking way.
Norman Jayden: ISTp - a capable investigator with great attention to detail. Holds his own in physical fights despite being bodily unimposing. Initially seems to lack Se but flares up when the need arises.
Officer Blake: ESFp - highly aggressive, quick to judge, trigger happy. Gets in trouble for being too brash about things. Tries to finger innocents to get the investigation out of the way. Very good at playing social power games. Portrayed as a villain.
Lauren: INFp - another sensitive character, but far less mature in her attitude than Ethan Mars. Carries herself quite youthfully. Generally too melodramatic to be ISFp and too subdued to be ENFj.