Finally a solution that works without having to make any changes to the server:
Download the latest jsch.jar as Yvan suggests: http://sourceforge.net/projects/jsch/files/jsch.jar/ jsch-0.1.52.jar works fine
Place the downloaded file in your "...\JetBrains\PhpStorm 8.0.1\lib", and remove the existing jsch-file (for PHPStorm 8 it's jsch-0.1.50.jar)
Restart PHPStorm and it should work
Use the same solution for Webstorm