Please read the XXII Amendment, and show me where it prevents Bill Clinton from being VP.
Obviously, as long as those two maintain the fiction of cohabitation, they can’t run together (because electors cannot vote for two people from the same state) - but the XXII clearly is not a barrier to Bill as VP (or Obama, for that matter).
What’s interesting about Clinton’s situation is that the 22nd Amendment only makes two-term presidents ineligible to “be elected to the office of President.” But is Clinton allowed to serve as president? For example, what if Clinton were the Democratic nominee for vice president, and his party won? If his candidate couldn’t finish his/her term, could Clinton be president again? Or would he be unable to serve as vice president in the first place? For now, this is an unresolved question.
http://www.infoplease.com/askeds/presidential-term-limits.html
Amendment XII already says that a VP must be constitutionally eligible to be President, and the Twenty Second Amendment did not alter that requirement. Clinton is not eligible to be President under Amendment XXII, therefore he cannot be Vice President under Amendment XII.