Yes, they are fully interchangeable. They share the exact same back case and window lens. The front cases and keypads are the same size between the two models. The difference being the color of the front cases, and the color of the keypads. I believe the silkscreening of each key function is the same on both front plastic cases and keypads, so everything will match up just fine.
You'll need the following parts, which you can order from Uniden by calling their parts dept at (800) 554-3988:
GCAS4E1232Z - 346XT Front Case
KDPZ4B9811A - Display Window
RCUN4C0405Z - Window Foam Gasket
You may want to get a new speaker also, as they are glued into the front case. This way you can leave the 396's front case intact if you want to switch it back (it's easier to solder the two wires than it is to remove the speaker):
BSPG0590001 - Speaker
I don't have the part # for the 346XT's keypad. You'll have to either use the 396XT's keypad, or see if Uniden has the part # for it.
See this thread for more details:
346XT front case cracks