The operations in Iraq and Afghanistan (you describe) will be conducted under Article 3 of the Convention (only the first part has been reproduced and you might have to read the other clauses):
Article 3
a) This Convention shall be applicable only to civil aircraft, and shall not be applicable to state aircraft.
b) Aircraft used in military, customs and police services shall be deemed to be state aircraft.
c) No state aircraft of a contracting State shall fly over the territory of another State or land thereon without authorization special agreement or otherwise, and in accordance with the terms thereof.
Under Article 3, no SARPs apply.
The conditions under which operations are conducted for the DoD are dependent upon the contract. If the contract require them to apply the conditions of the FAA 135 certificate (and OpSpecs), it will be stated.
Jim