Add a sign-in mapping for you website to your Xpages application. Point it to a custom loginform, for example the one in the xpages154.nsf.
Then edit the custom loginform and add the following line to the HTML Head Content :
(Sorry, I can not post this code here, so take a look at the image)
This way it will redirect to the main page and using the url parameter it will popup the login dialog again. The user isn't told the session has been timed out but that is something you could add yourself by (for example) adding another url parameter.