One way to do it, is to search for the music, you want to listen to offline, in Apple Music Classical, say Mozart Piano Concertos No. 19 - 25. Then you add those to a Playlist in Apple Music Classical. The same Playlist will also appear in standard Apple Music, where you can download it into your Music Library to make it available offline. There might be other ways to do it that I am unaware of.
As I have mentioned above, I just don't like this cross functionality, because it mixes up my Classical and non Classical music. I don't see, why they did not keep them completely separate. But at least it provides an option to download the songs onto your device.