As the Guardian said, most of the elders that have been involved in that discussion believe that each demon would block, so discarding multiple cards is possible. I know that the exchange happens first, as TitF is triggered and triggered abilties happen after other EC abilities.
Based on our discussion, I would rule that you still get to discard, but like I said, our proposed definition of blocks has not yet been confirmed by Rob.
Another issue: I'm pretty sure the Play As on TitF is wrong, nothing on the card says the Hero is protected from Healing, just the enhancement (which in most cases doesn't matter anyway, unless a healing card has an extra ability of discarding evil enhancements). Interestingly, however, The New Covenant can't discard TitF from an NT Hero, since it is a Healing card. Funny how that works.