Someone PM'd me this question and I figured it'd be of interest to more than one ;)

Find the line in the corsix-th configuration file:
-- audio_mp3 = [[X:\ThemeHospital\Music\]]

Remove the '--' which comments it out.
Set the location to where you have the music files extracted.
Play the game - with the MP3s there it will override the built in midi music ;)

For dumber ones such as me, the config file location can be found here:

http://code.google.com/p/corsix-th/wiki/ConfigurationFile

Users should also note that smpeg.dll must be present in the CorsixTH folder.

In case it is not, you can download it (e.g. from http://download.corrupteddatarecovery.com/download-file/smpeg.dll)