Two ordinary telephone lines.
Let's say you wish to have the live/recorded show done in New York, with talent chiming in from Chicago.
Chicago talent's audio is fed by Tie Line/Comrex or similar device to New York.
New York talent audio (i.e.: a mix-minus feed) is fed back to Chicago by ordinary telephone line, off an ordinary coupler into a headphone amp for the Chicago talent to hear New York. Since you arn't recording New York audio in Chicago, it doesn't need to be great quality, just intelligible.
The digital feed will have some delay, but it is only going one way. If it is a one-time only deal, you can probably rent the equipment. Even if this is an on-going project, once you buy the equipment it's yours. If you used ISDN, there is the additional cost of that line & the difficulty of getting it installed. The Tie-Line, and some of the other units can be set up for either POTS audio or ISDN, although these multi-mode units are more expensive
Another method, if you are recording a show for later broadcast, is to use the method NPR has used in the past.
You run recordings at both Chicago and New York. Chicago talent gets New York talent audio over a POTS feed to headphones, and this is recorded on the right channel. Chicago talent's mike goes on left channel as a clean feed.
In New York, the New York talent send their clean feed to the right channel, while Chicago talent audio comes in by a second telephone line and is fed to New York talent headphones and to the left channel recording.
After the session, you simply combine both recordings, keeping the clean feeds on left and right channel and discarding the telephone audio. Easy to do with digital editing, NPR used to do this on a pair to tape machines.
Of course, if you have a more complex show with music elements then either multi-track record (if you have the software) or remix. Again, a lot easier to do in this digital age.