My guess is that you are using relative URLs in your header.php file. That would explain the difference in the paths. (It is probably differnt on archive pages too, right?) Don’t do that. Relative URLs do not work well in a WordPress context. Generally, you want to use get_permalink(), site_url(), home_url(), etc. to create absolute URLs. For the template files you want get_template_directory_uri() and get_stylesheet_directory_uri().
I am guessing that you are also not registering and enqueueing the stylesheets and scripts.
See:
http://codex.wordpress.org/Function_Reference/wp_register_script
http://codex.wordpress.org/Function_Reference/wp_enqueue_script
http://codex.wordpress.org/Function_Reference/wp_register_style
http://codex.wordpress.org/Function_Reference/wp_enqueue_style