Multiple sites from 1 install?

Multisite is a relatively new feature of “standard” WordPress (i.e. – not WordPress MU, which was built for large numbers of sites). As a result, there is not a lot of documentation for it yet. But I’ve been using it for quite a while and it works fine, and can likely address your needs.

This article is probably the best place to start, if you ignore the irrelevant (to your situation) parts, and follow the relevant links within it:
http://codex.wordpress.org/Migrating_Multiple_Blogs_into_WordPress_3.0_Multisite

But it can also be as simple as a site with the root as its URL, and two others in subfolders of the same domain name. Or all three in subfolders off the same domain name.

All three appear to be different sites because of the 3 themes but in actuality they would be one site with 3 distinctly different areas.

If you just want to have different “themes” for 3 distinctly different areas, you don’t even need to go multisite.

Simplest way is to create Page Templates or Category Templates then create 1 header.php, 1 header-second.php, and 1 header-third.php with respective stylesheets. You can call respective headers accordingly in Page or Category Templates with
<?php get_header(); ?>
<?php get_header('second'); ?>
<?php get_header('third'); ?>

You can work it that way for your footer.php, footer-second.php
and footer-third.php

References:
http://codex.wordpress.org/Pages#Creating_Your_Own_Page_Templates
http://codex.wordpress.org/Category_Templates
http://codex.wordpress.org/Function_Reference/get_header
http://codex.wordpress.org/Function_Reference/get_footer
http://codex.wordpress.org/Function_Reference/get_sidebar
http://codex.wordpress.org/Function_Reference/get_template_part