Here's a good pic of a Vette transaxle unit.
http://www.web-cars.com/corvette/photo.php?photo=DSC_2704_a.jpg
and the website gives some decent pics of the drivetrain layout
http://www.web-cars.com/corvette/1997-3.php
Essentially, the engine still carries the clutch, sends power down the driveshaft (encased in a torque tube) to the input shaft of the trans. Output of the trans (Tremec unit) goes directly into the axle assembly (Getrag unit), and through the limited slip diff.
I have a pic somewhere of what the torquetube looks like, but it was taken after we turned it into a coatrack..

The Corvette setup is not unique, search google on Porsche 944 transaxle. Similar layout, except the differential is in front of the trans, so power comes from the engine, down the driveshaft, under the halfshaft centerline, into the trans, and then power comes back out the front of the trans to the diff.
The automatics just have a flexplate on the engine, the torque converter is on the input shaft of the trans. So, manual trans clutch in front, auto trans torque converter in back..