I have done this by playing the music DVD with PowerDVD, and recording the resulting audio thru the wave out mix of my soundcard.
This approach requires an Audio recording utility such as Audiotools.
http://www.unrelatedinventions.com/Audiotools/index.php
This is a record directly to disk program, that offers file conversions, (.wav to mp3, mp3 to .wav, mp3 to wma, etc. etc.) This is a very powerful program, with many other features. It is only $25 US, and offers a generous trial period. Help section is in laymans terms, and support from the author is timely.
(not trying to promote this program, just stating what's worked well for me)
My results with this method have been excellent, however it does require playing the entire DVD, such as you would if recording a LP or cassette to your hard drive.
I have never tried it, but the suggestion in post #8 looks as though it has merit, if it allows ripping of a separate file for the audio portion of the disk.