The problem is that I had my headphones on. So, now, when I play the recording, all I hear is my voice and not the other person's voice.
GarageBand will not have recorded what you were hearing in the headphones. You were recording, what the microphone was picking up, and that is only your voice - I think there is no hope to recover what your interview partner said.
In the future, and for anyone reading this looking for help always test new software, setup or gear before you use it in a project.
Also most podcasters that record remotely will have the remote person also record their end of the conversation. The file is then shared and synced with the interviewer's audio track. And if you don't want to mix the extra track you always have a backup.