It is Iraqi airspace but US defended under the terms of the joint forces agreement. If Israeli fighters tried to overfly and the Iraqis requested it the US would be bound under the treaty to stop them by all means. It is not actually US airspace but it is US controlled airspace. It is only by this treaty that the US is able to conduct operations in Iraq legally so they are unlikely to breach it.
Clashes between IDF and protesters in Bethlehem and East Jerusalem (Reuters)
from the article: Brzezinski: U.S. should forcibly stop IAF flying over Iraq to reach Iran