When was the Department of Defense put in charge of health matters?
They're not. if you read the report, it discusses how they handle the loss of manpower and resources necessary to maintain force. It's normal for them to periodically assess what would happen if... and how they would continue to function in those scenarios. The discussion assumes they have to support civilian population because of the mass casualties and because they are so very, very dependent upon the civilian population and manufacturing base for their support.
Why was the country's response to the flu classified in the first place?
First, this is a military response plan to a pandemic. Some aspects of a military response would, of course, be classified. Second, they don't want to induce panic. Or engender complaints. A simple example... They might leave out the lines that read: "Mass casualties are to be placed in pits, the bodies burned, and then buried using available backfill material."
6.023 x 10 to the 23rd power alligator pears = Avocado's number