The rules state that they have to be considered a "household" because they live in the same residence. She could ask to be considered a separate household but she would have to prove that she is a separate household and pays for food separately.
So, if she did say she was paying rent, then she would have to claim her husband's income. He was a PFC 6 years ago. So, he's probably an E5 or E6 now. That might qualify for WIC but I'm pretty sure not for food stamps (based on what I know of the military.) Also, at some point, if anyone found out that she was living with JI, she could be prosecuted for welfare fraud. Of course, I don't know how well they enforce that, but it could happen. lol
Based on my neice's experience in Kansas, if DB applied for any kind of welfare by saying that she was separated from her hubby or whatever, they would make her jump through hoops... such as taking classes, etc. DB would be expected at some point to actually start working. My neice tried to sit on her butt and collect welfare and they kicked her off because she didn't take the classes she was supposed to.