Here's my two cents worth. I found this to be a very interesting topic so I looked up some statistics online and played around with some possibilities.
From this survey, it appears that approximately 40% of those who responded had fathers in the military while 60% did not have fathers in the military. Is this 40% a greater percentage than would be expected in the population at large?
For sake of simplicity, even if we assume that all who responded are US citizens (probably not true) and that this is an unbiased sample (maybe not true), this is not an easy question to answer.
The weighted average of Total United States Military Recruits: Army, Navy, Air Force (per capita) is 1 per 2,000 people (or about .05% of the population). Males make up about 80% of the military. So males in the military make up about .04% of the US population.
To examine just the fathers eligible to serve in the military, we would have to rule out about 25% of the US citizens who are under 18 years old and cannot serve, all females over 18 years old - about 38% population, and all the males over 18 who are not fathers - about 17% of the population. So now we are talking about 100% - (25% + 38% + 17%) = 20% of the US population are fathers who could potentially serve in the military.
While males in the military make up about .04% of the population, it is likely that about 5x's that many fathers are military fathers. So about .02% of all fathers are military fathers. If this is correct, then the 40% found here is considerably larger than the .02% expected in the population at large.