This is a tough one... My mother was the same way.
Take the time to sit down with the father (and a recruiter, if optional/possible) to explain the lifestyle and pay/benefits. Ensure that you have answers to any and all questions he may have (hence the recruiter's presence).
Keep in mind, and explain to the father, that service is the armed forces is a noble venture. Mention family members who've served and use this as a stepping stone. He should take great pride in his child's wish to join the military.
In the end, though, the child's life is their own, and he/she must be ready, willing, and able to make their own decision. If this is what he/she truly wants to do, they must be prepared to go the distance.
I wish the potential servicemember the best of luck.