There are methods for displaying and tying into vBulletin data on external pages. Much of it is documented on vBulletin.org, amongst others.
However, you may not be able to put it on an HTML page. It will be PHP code, meaning that you either:
- Make php pages, not html pages, -OR-
- Run html as php on the server. This can be done, but is often not suggested for various reasons.
A php page can hold pure HTML code.
I do it for includes on one of my new sites, because this helped me cheat a WordPress crossover. Having the menu.php stored in the theme directory, I can now directly access site-wide menu from with WordPress, instead of having to edit the external html file separately. I've replaced the standard WordPress menu with a JS-powered one, a manual fix. The WP CSS version only displays when a person has JS disabled in the browser, or is running NoScript with the site not in the exceptions list. It also includes the warning "please enable Javascript to view the site as intended" -- or something to that effect, still writing it.
As far as login-specific suggestions, I saw one at daniweb, although it fails to mention the version of vB and is from early 2008. See
http://www.daniweb.com/forums/thread109707.html
As with anything else "crossover" in nature, you may just be in for a wild ride here, ending up with nothing functional after investing a lot of time in such a "hack". Just be warned.
Sometimes it's better to just include a link to the login page. For example,
http://www.digitalFAQ.com/forum/login.php and then be done with it