Most people want to go the other way from what you are trying to do. They want to combine the multiple disks into one album. But it is also very easy to separate disks into separate albums, using the appropriate tags.
MC defines a single album using the Album Artist (Auto) tag and the Album tag. An album has all the album and album artist (auto) tags the same.
The first view you show indicates that Album Artist (Auto) and Album are the same. The disc # tag separates them into separate disks, all within one album.
To get the second view, you need to indicate to MC that the tracks are separate albums, which means either Album or Album Artist (Auto) are different. One way to do that is to change the album names for each disc, in this case to something like Two - Disc 1 and Two - Disc 2. Alternately, you could change Album Artist to different names for each disc, which would change Album Artist (Auto), since the Album Artist tag overrides the automatic calculation of Album Artist (Auto).
You can easily set the cover art for each track, simply by highlighting each track and adding cover art. However, for a cover art view, the first track cover art is used for an album. So, you will only see the cover art for the first track. Once you separate the tracks into two albums, then the cover art for the first track of the second disc will become the cover art for that disc.
