This is point that was made in an article by Rosa Brooks in Foreign Policy:Welfare State, Meet America's socialist military, July 19, 2012. It's not that the actual troops are receiving too many benefits, but that the Army is being overrun with single moms. This is a point first made by Stephanie Gutmann in her book The Kinder, Gentler Military: Can America’s Gender-Neutral Fighting Force Still Win Wars? in 2000, and made again by Kate O'Beirne in 2003, during the Jessica Lynch business. [An Army Of Jessicas, May 19, 2003]
This article asks
How Well Does the Military Treat Single Mothers?Nicole Allan, Atlantic Wire, Feb 12, 2010
On Thursday, the military decided not to court-martial a single mother who skipped deployment to Afghanistan to avoid placing her child in foster care. Alexis Hutchinson, formerly an Army cook, received an other-than-honorable discharge. Her rank has been reduced to private and she will most likely lose her benefits.
The 21-year-old Oakland native arranged to leave her 10-month-old son with her mother when she learned she was deploying to Afghanistan. After caring for the boy, Hutchinson's mother decided the arrangement was not sustainable. Hutchinson claims she could not find an alternative caregiver and that the military told her she should put her son in foster care. Army officials, however, claim she had no intention of deploying in the first place.[More]
Here's a picture of Alexis and her son:
"Skipped deployment" is one way of putting it, and the New York Times called it "what might seem natural to a parent but to the Army was a serious offense", but readers with military experience will remember it as "AWOL, Missing Movement "—she didn't get on the plane, so her unit flew to Afghanistan without her.
For an actual soldier, this is a very serious offence. It's true that her unit was probably better off without her, but that was not her decision to make.
It's more of the military as a welfare state—if there were an actual war on, the question would not be "How Well Does the Military Treat Single Mothers?" but "Are Single Mothers Any Damned Use To The Military?"