I not quite sure I understood your question, I just hope I can help:
The server hides the /filename when it is the default one, index.html or index.php or default.html or something of that kind.
You say you have two sites on the server.
I don´t know you service provider but with cPanel in some accounts types (not dedicated) inside your public_html folder you should see a directory called "your_second_sites_name.com" and there you will have and index.html that would be your second´s site public_html.
I hope this helps you out if no, please add a comment and I´ll gladly edit my answer! good luck!