In a word, no working captured firearms.
I consider myself an authority on the matter after this Iraq deployment when this question was asked and I researched the heck out of it.
General Order #1 prohibits the personal possession of personal firearms and munitions in Iraq and Afgahnistan and presumably elsewhere. With notable exception to Afghanistan in 06, when pre-1898 "antique" firearms could be purchased on the market and brought home under an exception to the General Order. However, then there are customs issues and possibly ATF issues and then homestate issues (if any).
For a Servicemember to be able to bring home a weapon, he'd need an exception to the General Order #1. That's generally a nonstarter. Assuming he got that, he'd need clearance from customs. And then any other pertinent federal and state agencies.
Now, a Battalion or larger size unit can accept a gifted weapon on behalf of the US Government, but there is a lot of paperwork involved and sadly the weapon is permanently demilled. They weld a steel rod in the barrel, weld the crown shut, remove the firing pin, and welt the bolt shut. The are letters from the Command, gifting unit, a legal review by JAG, and then off to customs for authorization. A real PITA for a wall-hanger.
Sad, really on several counts, to include the fact that Uncle Sam is so paranoid about servicemembers bringing home bolt action rifles and handguns.
Now, as to bayonets and other non-weapon memorabilia, there is an allowance for this stuff - but it also requires approval paperwork from the Command.
Also - I will add to tell your friend to distance that thought from his head about bringing home a firearm. No legal way to do it for most folks. And he should never consider smuggling it. He will get caught. Customs is so thorough they make everyone feel violated, frankly. And customs is on to the tricks and gimmicks. After a decade they got pretty good at finding hidden compartments, false box bottoms, the 'firearm in the printer', and mailing a rifle home in pieces. Everything is searched and Xrayed and a $300 firearm isn't worth prison or a dishonorable discharge.