[..] I would like to redirect them to some specific .html when hitting home.
A language like PHP is better suited for redirecting a single page.
The following code will redirect http://example.com/ to http://example.com/example.html and http://example.org/ to http://example.org/anotherpage.html. http://www.example.com will be unaffected (note the www. part)
RewriteCond %{HTTP_HOST} ^example.com$ [NC]
RewriteRule ^$ example.html [R]
RewriteCond %{HTTP_HOST} ^example.org$ [NC]
RewriteRule ^$ anotherpage.html [R]
The first line matches the HTTP Host field (a.k.a. 'domain') against example.com case-insensitive (^ marks the beginning of the string, $ marks the end).
If there is a match, the page will be redirected (second line, [R]) to example.html
The same story for the third and fourth lines.