Is there any way in which you can have another faculty member, or someone else you trust, take a look at your advisor's letter? Are you using a dossier service of some kind that would allow that kind of check to take place without your advisor's knowledge?
Will an application in the Humanities without a reference form the Ph.D supervisor raise red flags?
I haven't served on a search committee, but my gut instinct is to say that the absence of a letter from your supervisor will raise red flags, but that those flags wouldn't disqualify you from the interview stage -- especially if, as you suggest, you can fill your dossier with sparkling letters from other faculty members.
As you've already seen, having this letter in your dossier can prevent you from even reaching the interview stage. If talking with the advisor about this really isn't an option, then I'd suggest not including the letter in your apps, and trying to think about how you'll put a positive spin on this situation in an interview.
I do think that it would be wise to talk to your advisor at some point, since the committee may try to contact hu before or after an interview.