Brenna-
I spent the month of April 2003 in Baghdad. I can't really speak to the safety of the green zone since it didn't exist when I was there. I will try and give you some idea though.
First of all, it depends rather heavily on what your dad will be doing. Driving around outside the green zone (for instance if he lives in the green zone but does his work outside it) is less safe. Living and working in the green zone should be relatively safe. About all he has to worry about in that case is indirect fire, mortars rockets etc... coming in from outside. The terrorists are less likely to use those because the Air Force is very good at smearing the launch sites within a second or two of the launch and patriot batteries(anti-missile) are very effective, resulting in a limited return on the (dead)terrorist's investment.
Remember, there are about 130,000 troops in Iraq right now and only about 1500 have died there in the last year and a half. Now delete all those that died from direct enemy fire, they don't count in this calculation. (unless you're dad's in one of the combat arms, infantry, mech infantry, Special Forces etc... in which case the danger goes up in some ways) Take the number left out of the 1500, divide it by 130,000 and then by three (6 out of 18 months) approx .002% chance he'll be hurt. All the other mitigating factors, which basically center around what his job will be, make his chances even better.
I suspect that if you look up some statistics on the internet you'd discover that there are many things more dangerous than being a support soldier in Iraq right now, like driving.
The reason I say his being in the combat arms ups the risk in only "some" ways is the following. Combat soldiers go out where it's more risky more often than straight support soldiers but the terrorists really don't like attacking them because they always get their asses handed to them. Example, Fallujah.
What is he going to be doing? (reiterate Jeffe's post)