Make sure that the contact at the company is listed in the client "contact" section of the file.
You will also need to make sure you have giving them access to view there files, this access can be modified in "Roles and Access" in the settings.
Go to setting>roles and access (for client)> and make sure that "case detail" module is set to at least "Low".
Also make sure the case you would like your client to see is Viewable to client. This can be changed when you are first entering the case in the system or can be accessed by clicking the "Edit Case" button from the Case Details page.