FWIW, this is what I've experienced with trying to connect my phone to my computer... I have a 32GB microSD card that I bought for the OG Evo, so when I got my new Evo, naturally I popped that in.
When the phone is connect to the computer, if I choose "Media sync", then both the phone's internal memory and my SD card can be seen as separate drives. However, not all of the files on the card are detected by the computer--None of the pictures I took with the phone show up, for instance. But the movies that I had saved on the card previously show up. HTC Sync on the computer does not detect the phone.
If I choose "Disk Drive", then only my SD card shows up, and all of the files on the card can be seen. Card is temporarily and automatically unmounted on the phone, is remounted when I disconnect the USB cable. HTC Sync on the computer does not detect the phone.
If I choose "HTC Sync Manager", the USB Debugging mode is turned on automatically, and HTC Sync on the computer detects the phone. Both the internal memory and the SD card show up as separate drives, but still not all the files on the card are accessible.
AirDroid currently does not support reading content on the SD card. I've asked. They're working on it, however. I don't know if this next issue is true with all Evo LTEs, or just me, but when my screen turns off, the connection to AirDroid is lost.
If you don't see your files on your external card when connected in "Disk Drive" mode, I suggest you get a microSD adapter so that your computer's SD card reader can read it. Then, when you need to access/transfer files, simply unmount the card or turn off your phone, and read the card directly.