Nope, he's wrong. It says right in the spell description, at the bottom;
"Death Ward does not protect against other sorts of attacks, such as hit-point loss, poison or petrification, even if those attacks might be lethal."
As well, it states in the Unholy weapon info that Unholy Blight is the spell used to create this weapon and it states nowhere in that spell description that it is a negative energy effect. It does state that it "calls up unholy power to smite your [non-evil] enemies." So, by my reading, it is unholy damage drawn from the evil deity, rather then negative energy drawn from the Negative Energy plane.
Is the damage from an Unholy Weapon inflicted upon a good character (the bonus +2d6) negative energy damage? One of my players had death ward up on his character and thought that it was but I could not find a reference saying that it was.
The damage type is, well, unholy. That means that energy resistances and certain types of damage resistance won't affect it. I don't have my DMG in front of me, but I know that it is most certainly not negative energy; it does give the wielder a negative level if they are good, however.
I'm with Gwydion. The Anarchic, Axiomatic, Holy and Unholy weapon enhancements all give "an extra 2d6 points of damage against all of X alignment type" (paraphrased). Since it's bonus damage and not type-specific, resistances do not apply, though DR might. Note that these enhancements DO change the weapon alignment, and may as a secondary effect adversely affect wielders of opposite alignment.
That brings up an interesting question. If a paladin or other LG character picks up an Anarchic Unholy Longsword, does he gain one negative level, or two? Just a thought... I'm not trying to thread-jack the OP.
The bonus damage is untyped; it is not prevented by death ward, and it does not bypass damage reduction (though it does help overcome it by simply dealing more damage).
The negative levels do stack, so a LG character who picks up an anarchic unholy longsword gains two negative levels.
Joex: death ward does prevent hit point loss, as long as the loss is due to a negative energy effect (for example, an inflict spell). So it would prevent the extra damage if the extra damage were "negative energy damage." But it's not. Neither is it "unholy damage," or "profane damage," or "green damage." It is untyped damage.
The bonus damage is untyped; it is not prevented by death ward, and it does not bypass damage reduction (though it does help overcome it by simply dealing more damage).
The negative levels do stack, so a LG character who picks up an anarchic unholy longsword gains two negative levels.
I thought so...
My two cents: Unholy damage is unholy damage, not negative energy. Death ward won't block it.