A Web site has nothing to do with "Project Solutions" (what is it, by the way?). Project and solutions are just the artifact of development, they don't exist after you deploy the site code. The thing is: yes, the code-behind code needs what you call "physical paths"; more exactly, file path names in terms of the server's host file system. Such path names are obtained using the method
As to the sharing some files between-who-knows-what, you can do whatever you want, with one important limitation: usually, the Web applications are executed by the HTTP server software is some sandboxed environment. It won't allow access to to any files except those placed under the directory which is set up as a root directory for your site.
If you want to share some files between too different sites served up in the same host, without overlapping of the file paths, sharing the files is rather difficult. First work-around which comes to my mind would be the use of hard links
(don't mix them up with .lnk files; nothing in common). Please see: http://en.wikipedia.org/wiki/Hard_link
If this is the case, it's better to avoid such difficulties. For example, you can always formally merge too formerly different sites, as soon as you serve them up on the same host. As you did not clearly explain your sharing problem, I think this would be enough for now. :-)