According to a recent study more than a quarter of the US military's enlisted members suffer from an undiagnosed mental illness. These are predominantly mood disorders such as Major Depressive Disorder and personality disorders such as Intermittent Explosive Disorder. These are the results of a self-reporting study and there may be a significantly higher rate of mental illness due to self-image and avoiding detection. This explains the high rates of suicides among service members and veterans, sexual assault, and mass shootings. Although combat and PTSD complicates the ability to make this determination it is clear that those suffering from pre-existing conditions are also more prone to PTSD.
There is no convincing evidence to show that service members have a higher rate of undocumented mental illness than the general population. To say that the military's problems, various as they are, are a result of this is a gross oversimplification. The problems are a result of policy, politics and hundreds of years of institutional culture.