From the context, that it is a verbal exchange overheard, I would suspect that what you have is either a pun or an alternate pronunciation.
The country of Iraq is pronounced two distinct ways. The first sounds like "eye rack" the second sounds like "a rock." The question about what "arm" is probably an attempt to ask which "arm of the service." I am not sure but this usage is probably more common in American English than in British English. Webster's carries a definition of "arm" as a "functional division of a group," but the Oxford Concise does not.
Translating into a more idiom free English I suspect that conversation had the following meaning:
- It is from my husband, he is in Iraq.
- So is mine.
- What branch of the service?
The other alternative is a pun. A common joke about someone in the middle east is being between "a rock (Iraq) and a hard place" which is derived from a common American phrase for a difficult position being between "a rock and a hard place." Such jokes tend to generate jargon which is essentially an extension of the language used by a small group of people related by some field of study or situation. The Armed Forces is renowned for its jargon.