I was told recently by someone working with DoD equipment that although USB flash drives were banned, certain USB hard drives were still OK. He was telling me this because it was so hilarious and alarming.
I was talking to a guy who makes "encrypted" USB drives at the NSA TCC recently. It sounded scarily hand wavy to me. I was asking, "but where is the key stored" and he tells me with a straight face, "right on the drive".
My experience with these is that you must either use your PKI certificate or a password as the key to decrypt the drive. The default configuration is generally to use the PKI certificate on the chip embedded in your ID card. Since you have to have that card in your computer to be logged in to begin with, using it to access other stuff is essentially effortless.
The hard drive has to be scanned by an administrator before you're allowed to use it (not sure what this process entails). It also has to be encrypted, and won't mount unless it is encrypted with the proper DOD-approved software.
As far as I know, SSDs are not allowed, only magnetic drives.