It's Thursday night in Moscow; Linkin Park are playing at the premiere of Transformers: Dark of the Moon at one end of Red Square, in the shadow of the Kremlin. The gig security consists of lines of military policemen. Suddenly, screens begin showing nuclear explosions, and the giant, troubled face of J Robert Oppenheimer – the physicist who worked on the atomic bomb, then agonised over what he had created. As we hear him intone "I am become death, the destroyer of worlds", thousands of Russian fans suddenly hold up placards, reading Wisdom, Justice and Love.

The gesture – at an event taking place yards away from the seat of cold war power for successive generations – is given its power because it wasn't set up by the band, or their record label, or the film company, but by the fans themselves, virally, via messageboards.

"That totally threw us," says frontman Chester Bennington. "I had that same thought, that here was an American band playing politically, emotionally charged music next to the Kremlin. I could feel the weight of years growing up and being told that this was an off-limits place. So for kids to express themselves in that way was really moving; something that we will never forget, because it was unbelievable."

It's a conversation you'd expect to be having with U2, perhaps, not a band whose 20m-selling debut album, 2000's Hybrid Theory, made them commercial kings of nu-metal, a genre synonymous with screaming rage and very loud guitars. But today's Linkin Park drive hybrid cars, offset their carbon footprint and have taken a leftfield shift not unlike the one Radiohead took with Kid A. A process they describe as "destroying and rebuilding the band" led to last year's Rick Rubin-produced A Thousand Suns, a concept album about human fears, including nuclear war, featuring electronica and eerily beautiful songs such as Waiting for the End.

"When you come out of the gate with a record like Hybrid Theory, from a business point of view it's really dumb not to keep on doing that," Bennington says, all smiles, his big, black earrings and tattooed arms the only visual signs of his nu-metal past. "But we aren't a manufacturer. We are artists, and we've gone philosophically back to where we were writing music before we sold a record. When we were excited about a song, not because … "

Rapper and multi-instrumentalist Mike Shinoda butts in: " … This is going to be a hit!"

A week after the gig in Moscow, the pair – whose double act provides the band with its on-stage energy – are relaxing in the Mandarin Oriental hotel in London, where rock royalty often stay when in the city. Friendlier and funnier than one might suspect from the anguish of their music, they are as different from each other in person as they are on stage: Shinoda dry and thoughtful, Bennington livewire and open. But just as in performance, they spark off each other incessantly. Linkin's reinvention has been very personal for them both.

Shinoda is Japanese-American. During the second world war, his Japanese-born grandparents, who had emigrated to the US, were among the 110,000 Japanese-Americans interned in "war relocation camps". When Linkin were recording A Thousand Suns, Rubin suggested Shinoda write lyrics by stream-of-consciousness, and he found years of buried family memories suddenly tumbled out.

"Because it wasn't just the war," he says. "It was fear in their neighbourhood and everything, for years. My dad remembers being in school with my uncle, and the teacher would say outright to the class that the Japanese were second-class citizens and shouldn't be trusted. Before the war my family had a grocery store and a barber's shop, but after internment it was destroyed and they had to start again as strawberry pickers. But they won't talk about it. I wanted to tell these stories because nobody else will."

Bennington's past is, Shinoda is quick to point out, "more extreme". His parents' divorce when he was 11 led him to start smoking pot, which led to cocaine and methamphetamine. In some previous interviews, he has alluded to sexual abuse by an older male friend.

"When I was young, getting beaten up and pretty much raped was no fun," he says suddenly and disarmingly. "No one wants that to happen to you and honestly, I don't remember when it started. But about four years ago I went to visit my mom and I saw a picture of myself and I remember very clearly when that picture was taken. All of a sudden, because I had kids, I looked at it and thought: 'Wow, that's what I looked like.' And then I remembered. Oh my God. I remember that stuff happening to me at that stage and even thinking about it now makes me want to cry. Oh my God, that was fucking happening to me and I was just that little, much earlier than I'd remembered. My God, no wonder I became a drug addict. No wonder I just went completely insane for a little while."

Bennington's trauma fired Hybrid Theory and 2003's hit follow-up, Meteora. The success they achieved was, for Bennington, "like something you read in a book. It doesn't really happen. I followed my own instinct because everybody else was fucked up, and I didn't like anybody else's thing, so therefore I would do my own."

Although Bennington had knocked around in music for a while before Linkin Park came together, when success came, it came quickly. They realised things were changing when the pair drove over to Bennington's dad's house and heard their song on the radio. "It was the most surreal experience," Shinoda remembers, smiling at the memory. "There were multiple radios and we were on every one. It was like, 'Holy shit!' It was so cool."

Bennington went from sleeping in the back of an old Toyota to fronting what was then the biggest-selling debut album of the 21st century. Fans blared music outside his house. One woman caused a car accident after spotting him in the street. Bennington did not find the change in fortunes easy, and he fell back into serious drug abuse.

"Unfortunately, my ex-wife [Samantha, whom he married when they were so poor he couldn't afford a wedding ring] and I were really toxic for each other, too young to get married," he says. "We were volatile personalities, and even though we helped each other, we were not good for each other, and that brought up other feelings."

"The tours we did in the beginning, everybody we toured with was either drinking or doing drugs," Shinoda says. "I can't think of any that were sober. So you take someone who already has a hankering for drugs and … "

"I partied with everybody," Bennington says. That didn't help build bonds with the rest of the band – who were more into pot and booze, and had no idea their frontman would be sitting on the tour bus tripping. He says he knew what their response would be: "Fuck, man. Look at what we've got going here. What the fuck are you doing?"

It wasn't just the band who were kept in the dark. The early Linkin were a notoriously closed unit. Journalists would return from interviewing them with tales of confiscated mobiles and monosyllabic replies.

"We talked about this recently, and realised we were super-defensive," Shinoda says. The speed of their success led to suspicions they were manufactured, and for Bennington the accusation that he somehow "wasn't real" cut deep.

"I'm like, 'Fuck you, you don't know me," he spits, grinding a fist into his hand. "And personally I would want to jump across the table and fucking kill you. 'How dare you question what I'm singing about?' Eventually I thought: 'OK, you wanna know? This is where I come from!' and I told a journalist things I've never told anybody. And my dad – a policeman – rings me up and says: 'What the fuck do you mean this happened to you when you were a kid? Who did it?' And I was thinking: 'What have I done?'"

Eventually, Bennington revealed the identity of his abuser to his father. He realised his abuser had in turn been a victim and chose not to pursue him. "I didn't need revenge. I realised … "

Shinoda quietly finishes the sentence: "That it can end with you."

It did, but only after a lot of therapy. Linkin's metamorphosis began in 2007, when they hooked up with Rubin for the tentatively experimental Minutes to Midnight, after Bennington had turned his life around. "I'd become a person that wasn't me," he sighs. "This is me. I'm a nice, friendly guy that was always stuck behind this monster that was just really a hurt kid."

Bennington got divorced in 2005 – his ex-wife, the mother of his first child, has since become a "really great friend, and a great mom, and I regret every bad thing I've ever said about her in the press". On 31 December 2005 he married Talinda, a schoolteacher and former model. The relationship changed him, and with therapy, rehab and faith "unlocked all these things that I'd been carrying all those years". When Linkin returned to the studio, he found that his vocal style had changed from the previous roar to something less aggressive.

"I realised I didn't have that inner beast anymore," he says. "I didn't want to scream."

Linkin have since transformed their entire modus operandi. "If we'd made another record like those first two, we'd have made the same record until we split," Shinoda says, revealing that the band have also rekindled – and in some cases begun – intra-band friendships. "But we realised we didn't have anything to prove to anyone. Linkin Park can be as lyrically or sonically adventurous as we want."

"Music can be political in a way I never felt before – performing certain songs in Red Square or Tel Aviv can really affect people," Bennington says.

He still encounters problems – in 2008, a stalker called Devon Townsend was jailed after cyber-invading his life, accessing all his voice and emails and stealing hundreds of photos of his children. "It's not fun to put someone in prison,"he says. "Ninety-nine percent of fans are great. We're famous, but we're not celebrities. I can go to the grocery store and the post office. People say: 'You signed up for this.' No, actually, we signed up to make music, not to expose our families to crazy people. But now it's all about the music. And we're only getting started."

• The deluxe DVD edition of A Thousand Suns is out now on Warners. Linkin Park's Iridescent is on Transformers: Dark of the Moon's soundtrack