Looking up the reg (61.23) it seems the military pilot medical does apply in some cases.

11) When a military pilot of the U.S. Armed Forces can show evidence of an up-to-date medical examination authorizing pilot flight status issued by the U.S. Armed Forces and—

(i) The flight does not require higher than a third-class medical certificate; and

(ii) The flight conducted is a domestic flight operation within U.S. airspace; or

(12) When exercising the privileges of a student pilot certificate or higher while acting as pilot in command on a special medical flight test authorized under part 67 of this chapter.

Don't know if the OP is a military pilot transitioning out or just looking to get into aviation.