The 41-year-old actor and his singer spouse Leann Rimes opened up about their ongoing feud with his ex-wife - whom he infamously cheated on and then left for LeAnn - on the first episode of their new VH1 reality show 'LeAnn & Eddie', in which Eddie made the apocalyptic dig.
He said: ''The likelihood of Brandi and I getting back together, I would say, would be slightly above the existence of Bigfoot and just below an actual zombie apocalypse.''
LeAnn, 31, meanwhile, labelled the 'Real Housewives of Beverly Hills' star a ''third party'' in their marriage and claimed Brandi won't let the highly-publicised feud die.
Dispelling tabloid rumours of marital issues, she said: ''Well, it's unfortunate that we have a third party in this situation that's just a mouthpiece. It doesn't matter if we say anything because she'll keep blabbing about it.''
The couple also joked about the public's perception of them, with Eddie - who has two sons, Mason, 10, and seven-year-old Jake, with Brandi - admitting they are aware people ''think [LeAnn] is a homewrecker and a stalker''.
LeAnn quipped: ''You're forgetting alcoholic, pill popper and children stealer!''
The 'Can't Fight the Moonlight' singer then turned the tables on Eddie, humorously addressing rumours about him.
She added: ''And you're also a moocher, you have no job, and you married me for my money.''
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