I have exactly the same issue with images appearing broken after uploading into admin and not appearing on the site in preivew. I’m also using multisite.
My uploads path reads: wp-content/blogs.dir/8/files
BUT
when viewing the directory through FTP, the filepath where the images are uplaoding to is different.
This reads: /wp-content/blogs.dir/8/files/2011/10
The fileupload URL reads: https://mysitename.org/subdirectoryname/files
Not sure where to go next?