St. Jimmy noteAmerican Idiot doesn't explicitly say whether St. Jimmy was a separate character or an alternate persona of Jesus of Suburbia, but the first clue is in the album book included in the CD. The song lyrics are written as entries in a journal. On first page of the journal, the diary has a label establishing that it is "property of Jimmy", who isn't introduced until his eponymous track in the middle of the album. So JOS and Jimmy must be the same person.
Jimmy dies in "Homecoming", but JOS lives on. "Homecoming" wasn't a suicide note, since the date for "Whatsername" said January 1st, while "Homecoming" is dated October 19th. JOS is definitely alive and well and still writing in the diary. St. Jimmy's death is a figure of speech ("In the state of mind, In my own private suicide") for the character giving up his persona to turn his life around.
It seems that the real character of Jimmy initially thinks of himself as the 'Jesus of Suburbia', leading his group of friends. Once he leaves for the city, this doesn't work as he doesn't know anyone, so invents a new persona of 'Saint Jimmy' in order to start afresh. Whatsername shoots this down, essentially telling Jimmy to stop kidding himself, during Letterbomb. The Saint Jimmy persona is then symbolically killed off in Homecoming.
This is also alluded to early on in Boulevard of Broken Dreams. "I'm walking down the line that divides me somewhere in my mind." This is talking about to the split JOS experiences when he creates Jimmy as an alternate persona.