This question sounds to me like the difficulties of NAT Traversal and trying to establish peer-to-peer connectivity over the Internet. I stumbled on this question researching the best way to set up Internet connectivity to a device that is sitting behind a firewall. I am assuming that the device behind the firewall has to initiate the connection, that a Internet server application (on a Public IP address) to at least manage the initiation of the connection is required, and the Internet server application may also have to act as a relay if the difficulties of NAT is not able to be traversed.
http://en.wikipedia.org/wiki/NAT_traversal
http://en.wikipedia.org/wiki/Peer-to-peer
A good example of this is LogMeIn. Where the application is installed on the computer that needs to be accessible over the Internet, that application communicates with the LogMeIn Internet servers, you can establish a connection to that computer either by initiating through the LogMeIn servers and connecting peer-to-peer over port 80/443 using NAT Traversal (this would be establishing a peer-to-peer connection) or by initiating through the LogMeIn server and the LogMeIn server acting as a relay if peer-to-peer is unable to be established.
Please note; you must have an application (something running) on both ends of the connection on the Internet, there is no other way. Just like FTP that was mentioned earlier (FTP Client, FTP Server)... but in this case it is peer-to-peer (basically you are writing your own Client and Server... or if you have to use a relay... Client--Relay--Server
http://en.wikipedia.org/wiki/LogMeIn
"The service connects the remote desktop and the local computer using SSL over TCP or UDP and utilizing NAT traversal techniques to achieve peer-to-peer connectivity when available."
The part I don't know is can the relay go in both directions; and I am figuring the device behind the firewall must have to constantly manage the open connection to the Internet Server that is the relay. Those are the questions I am wrestling with now.
Also, you may want to check out this post.
C# byte streams through TCP