Of course there's a parent directory. In relation to the server, that folder you get dumped into when you log in is at /home/yourUserName/.
As far as your domain.com folder goes, as I unserstand (though I've never done it myself) is that you can just create it exactly as you set up the domain in Panel > manage Domains > add new. Then place an index file in the directory and it will work. If that's not the case, then for some reason other parts of the domain data didn't get set up server side.
Try going to Panel > Mange Domins > edit (across from the domain in question) and then click the thing to save changes - even though you didn't make any. Now wait up to an hour or so and see if you domain.com folder appears. If not I think you'll have to contact support on this one.
Please post back and let me know how it goes.