JohnBurke

If the NATOPS specified two pilots, or if the operation within the military specified two pilots, and if you were acting as a rated, assigned officer in a military capacity in that aircraft in that operation, then yes, you could log it.

Operations Specifications do not apply; you were not operating under operations specifications, and theres's not "OpSpec" equivalent. Operations Specifications are the provisions and conditions that the FAA applies to a Part 91 subpart K (fractional), Part 121 (airline) or part 135 (charter) operation. OpSpecs are not issued to the military, by the FAA and are, therefore, irrelevant. Your ATP is also irrelevant, as in this case, your ability to log that time depended on your military status.

You used the term "not at the controls," which is ambiguous. Were you saying you sat in a pilot seat but didn't touch the controls? Sat elsewhere in the airplane without access to the flight controls? Were assigned as a pilot, in a pilot seat, but not pilot flying?

If you're asking about a situation in which you were not a military aviator, but sat in the seat and didn't touch the controls, could you log that time as SIC because you held an FAA pilot certificate at the ATP level, then no...nothing about that operation would qualify you to log SIC (and I suspect claiming to be pilot in command of a military aircraft when not qualified as a military aviator, would be unwise). Remember that if your question regards whether holding ATP certification would play a part in the ability to log civilian time...the ATP allows you certain privileges if you weren't PIC, such as giving instruction in air transport operations...but that's not what you were doing, and is also irrelevant