The only simple-minded thing I can see is that you can set your CD player to autoplay, and theoretically you can designate different programs for the several kinds of disks. It may be that you only have a program set for audio CD.
If you can see the drive in Explorer while an audio CD is playing(?) you can right click to get Properties for the drive. The autoplay tab on the properties display has two choices, a button at the top that you click to put a dot in if you want to select an option to always play, or a button at the bottom that says "prompt me." If you want a choice of what to do, probably the lower "prompt me" button should be the one selected.
If you can't see the drive in Explorer even with an audio CD playing, you'll need to go to Start - Settings, double click on SYSTEM, on the Hardware Tab, open Device Manager, where you should be able to see how the thing is set up. Once you find the drive in Device Manager, you can right-click to see properties (but not the same ones as from Explorer). There is a place, after you right-click to the properties for the drive where you can elect to allow digital audio. If it's NOT CHECKED the drive may only read "audio" files, so clicking on the digital there may help it to see "digital" disks(?). There is a trouble-shooter on the General Tab that may help (although experience suggests it will probably tell you everything's fine).
As an aside, I've found CD/DVD drives to be one of the most troublesome things on my current machine. My DVD/CD-R/W is an early model, and it's given me persistent problems. After three consecutive driver updates, all promised to fix things, and multiple cleanings and adjustments, I'll probably be on my way to find a replacement drive within the very near term. I can help today if anybody wants a matched set of coasters - for a large party, since I was trying to burn some backups most of the night.