I'm very picky when it comes to music, so I probably wouldn't use Discovering Music for several reasons:
1) Naxos CDs are kind of cheap. They're not necessarily bad recordings, but they are rarely the best available.
2) No medieval or Renaissance music
3) I wouldn't listen to Schoenberg for fun, but I don't think that you can adequately study 20th-century music without touching on Schoenberg and 12-tone music. Overall, it seems weak on 20th-c. music in general.
(#2 and #3 are probably due to the fact that it only covers 300 years of music)
4) I'm not sure how much listening guidance there is. The one unit available for preview was on 19th-c. opera, and it seemed more focused on libretto, staging, opera houses, etc. Hard to tell if there might be more guidance in the other units. The "Viewing Guide" questions don't seem to focus much on actual music, either. Related to this, I'd like to have some listening quizzes, and I'm not sure that this program offers those.
5) I'm not a huge fan of video lectures. I'm also guessing that the video lecture format mainly uses excerpts, which I dislike (to me, listening to one movement of a symphony is like just reading chapter three in novel)
I think that some of the units look promising, though, and it might be useful for someone with little or no background in music. In my case, I feel like I have better recordings of the pieces included in the CD set, and I'd prefer more guided listening. And I guess for $139, I'd want a more comprehensive music history, not just 300 years.
Lastly, one nitpicky thing: the book individually lists a Naxos link for every composer in the unit under "Websites", which seems like a useless space-filler to me. Seems simple enough just to tell the student to refer to the Naxos page for each composer ...