There's no law that says someone can't record any conversation with another person (interview or otherwise), if the other person(s) involved have knowledge of the recording. However, there's also no law that requires anyone else to continue such a conversation (interview or otherwise) after becoming aware that you are interviewing.
In other words, if you want the interview and the employer doesn't want it recorded, then you either get the interview without recording or you don't get the interview.

