if they are asking for the cover then they mean the cover (for UK citizens, this is maroon). Take it, if you don't then they will think you have not read the email or paid attention to the detai.
If I were you I would copy the cover and the page with all your details on, then take the original passport and the photocopies with you to the interview. When we interview we have to sign to say we have seen the original, but keep the copies which will go on your personnel file if (when!) you get the job. As jb says, most employers keep data for equality & diversity records so they will need to see the cover to clarify which country issued it.