You mentioned a Cisco router, Cisco also makes a VPN client that you could use on your home PC. I use this every day I then connect to the network via the "Secure Tunnel" created between the Cisco Router and my PC. After that I have access to all the machines I have authorization to see. In effect this places my PC on the network.

And as to the original question yes they are all bi-directional (Full Duplex) capable. But most of the time in a situation like you are describing traffic flows in one direction mostly with only "ACKs" (acknowledgements positive and negative) being sent from the other side.