From what I remember the government sends classified information through the US Postal Service. The item must be first wrapped in plain brown wrapping probably with some tamper detect and then put in to the mailing envelope. Then the mail is sent REGISTERED with RETURN RECEIPT REQUESTED and with a signature required (it might have to be sent and signed by a specific person). Thus there is tracking of where things went and the "package" is locked away each night in a secured area.
If the government uses this process for classified material, I'm sure its probably safe for transmission of unclassified but protected and sensitive information.