So it seems that you just want to insert -dir- between the containing directory and the file itself. I don't really understand why you'd need to do this though. A url_rewrite or even a "container page" to display include files should suffice, e.g.
Which could be url_rewritten to
I'm assuming that the directory name and the file 'name' part are the same from your example...
The displayfile.php would have...
$dir = clean($_GET['df']); //clean should be a function to strip any dots and forward slashes etc
$file = $dir . '.html';
$search = 'myfiles/$dir/$file';
include($search); //displays the file
//this means that all html files under myfiles would be publically accessible
The .htaccess could be:
RewriteRule ^show/([^/]*)/$ /displaypage.php?df=$1 [L]
Again, this is off the top of my head in 5 minutes - so not thoroughly thought through.