Only one process can listen on a particular IP:port combination, regardless of DNS. If you only have one IP address, and both sites must be accessible on port 80, you've got problems.
If you really can't get a second IP address or port, you will have to run a reverse-proxy on port 80 to listen to incoming connections, pick out the
Host: header, and redirect the HTTP request to the appropriate server (which will be running behind the scenes on a non-80 port).
This could be a third server, or one of the existing servers if they have the ability to work as a reverse proxy (eg IIS with ApplicationRequestRouting.)