I got it now, and you did too actually. It is all what RSS (the format in which the content of blogs goes from server to server, or actually web entity to web entity) is about...
It is called syndication, the same way you can use RSS to feed your blog, you can use the same RSS to have someone syndicating it for you to millions other bloggers, or you can also use the same RSS to get the feed on your email client, or to post a limited version of the content on yet another web site etc...
So I foreseen you being able to display the content of your WP hosted blog on your separate website using RSS, it is called consuming the feed. There are few things you need to get to know or get ready for:
1/ RSS is text, period (actually not quiet, but in our case here I am pretty sure it is). It means no widget, no template, no stats etc.. You will have to build the pages or place some sort of RSS client on your site that will consume your RSS feed(s).
Let's say WordPress is your secretary, when you are hosted here and are yourself in your office here, then you get full secretary service including coffee and housekeeping. However, from your hotel room in Paris all you will get from your secretary is call forwarding.
Well, the secretary is WordPress, you are the client, your existing website is your hotel room in Paris and call forwarding is RSS ;o)
2/ You need to check with the staff here what kind of feed you can get, you want one where
a) articles are not truncated, meaning you get the whole thing on the other end of the tube (your site) because sometimes RSS feeds only provide the first lines of each articles and then link to the full version on the original blog, which is helpful when you are the author and want people to come to your site at one point but not so when the author is actually the consumer of the feed... like you are!
b) comments are also provided (do you allow people to see comment on your site, and do you want them to see the comments?) That may be a problem because comments may not be part of the main RSS feed for your blog but I do not know, maybe yes. Ask the staff.
Hope this helps.