Hi,
Interesting idea, basicly the idea is to capture the input from both side and mix it on server and broadcast it to both or to anyone who want listen.
We'll have to research about the exact tech possibilities and implementation. However, I must clarify such a system will require good hosting (cloud / vps (no shared or low cost servers).
Digital ocean, Aws, Rackspace or dedicated box will be required.
Can you describe the user flow / features for us better understand how exactly you imagine this?
Note the price is only a rough initial estimate.
thanks,
Nirandas