URI with Slash

I have set the base url set to be 'http://domainname/public/'.  The links to css and js files are <link href="assets/css/..." rel="stylesheet">. Everything works well until I try to access a page with a slash in it, e.g. 'http://domainname/product/1'.  Now the path to the css and js becomes 'http://domainname/product/assets/css/...'.  The css and js files can't be found.
Why does this happen?