ENTP for sure...
The easiest way to tell is to look at the functions, not the letters. Sure, he comes off more as a feeler, because his feeling is extroverted, while his more dominant thinking is introverted, so you can't see it.
Fe: Watch Billie Joe in an interview or even on stage. He isn't monotone at all. Watch him in any interview and you'll see his eyes widen open and his eyebrows shift up and down. He's very open about his feelings, he cries on stage every time he plays Wake Me Up When September ends. Where as an introverted feeler either wouldn't cry, try really hard not to, or probably just wouldn't play that song. He's expressing his love and sorrow for his deceased father.
Ti: As Billie Joe has gotten older, his songs have become less childish and more serious. He's sarcastic and very political. Listen to 21st Century Breakdown and American Idiot. Both of these albums are mention a great deal of politics and in a way, bring up a sense of controversy. Examples would be the songs American Idiot, Holiday, East Jesus Nowhere, 21st Century Breakdown, The Eulogy, all of these songs have a key element of Ti and Fe working together.
Extrovert: This is almost too obvious. He's a total attention whore (no offense) but I mean cmon, he's the front man. He loves being the center of attention and pumping up the crowd. He barely even plays the guitar when he's on stage, he more or less interacts with the crowd.
Also notice how he dresses. The intuition is obvious, but also he'll dress in "cool" or punkish outfits (definitely perciever and Fe). Ever take a look at the 5 million tattoos he has?
ENTP's such as Newt Gingrich, Sacha Baren Cohen, John Stewart, Bill Maher all have the same general facial expressions, same general outlook on life, and even the same uniquely childish look in their eyes and smile that Billie Joe Armstrong has.
Long story short: ENTP