A windows system has a standalone java and is not recognized by the installer. A jar file can be run on the command line. Is the MultiBit linux jar and the windows installed one the same?
The Linux installer is slightly different to the windows installer in that there are different scripts to get the host machine to recognise the bitcoin URIs.
What ARE very similar is the multibit-exe.jar (used on Linux and Mac) and the multibit.exe (used in Windows). The exe is basically a wrapped jar file.
On any operating system you can run MultiBit jar file by running:
cd 'the MultiBit installation directory'
'path to java'/java -jar multibit-exe.jar
Make sure you cd to the install directory first as it uses that to pick up some files.