I am pretty sure it is church sponsored. It has links to Heart-to-Heart ministries. I agree that this is in itself not a bad thing.
My concern is that, especially in Iraq, this is ill-advised. First, there are obvious sensitivities. Second, there is always the temptation to use this to affect the religion of the region-even unintentially. This is a real danger for both the Americans and the Iraqi's.
There will always be the appearance that there is more than one reason that organizations like this are there. If they are either promoting Christianity, or acting as propaganda for the US occupation, this is a bad thing.
There are organizations that can meet the humanitarian needs in Iraq without a conflict of interest. I would suggest that Americans of all creed consider giving to the International Red Cross/Crescent or MSF (Doctors without borders). These are secular organizations with no competing or secondary missions.
I did check (with apologies I didn't check sooner) and it looks like although this organization is soliciting help from churches, it is trying to present itself with a purely humanitarian mission.
I suggest that others can do the job better. With groups like this, there may always be the urge to accomplish something more than pure humanitarian aims.

[from Foxfyres website]