For an experiment: don't run iTunes. Just put the CD in and see if Finder finds it and keeps showing the contents. I think it should (at least, a Windows PC does); to be sure about how OS X should behave, better ask on one of our Mac forums.
The strange thing is that it happens on three Macs. That practically rules out a hardware issue or a bad setting. So maybe it's a good idea to head to the Mac forums with your issue right now. Much more visitors, better help.
I installed iTunes 10 on three Macs. When I tried to import a music CD, iTunes could not find the CD. The CD would initially appear on the desktop and in the finder window but then disappear. This happened on all the Macs and with several CDs. With Apple's help I uninstalled iTunes 10, downloaded the program again and reinstalled it. No help. The one error message I saw said that iTunes could not convert the file track because it could not find the CD. Non music CDs (photos and data) work fine on all computers.