Must you use html file structure with JavaScript? Have you considered using PHP instead so that you can use simple PHP include object?
If you convert the file names of your .html pages to .php - then at the top of each of your .php pages you can use one line of code to include the content from your header.php
<?php include('header.php'); ?>
Do the same in the footer of each page to include the content from your footer.php file
<?php include('footer.php'); ?>
No JavaScript / Jquery or additional included files required.
NB You could also convert your .html files to .php files using the following in your .htaccess file
# re-write html to php
RewriteRule ^(.*)\.html$ $1.php [L]
RewriteRule ^(.+)/$ http://%{HTTP_HOST}/$1 [R=301,L]
# re-write no extension to .php
RewriteCond %{REQUEST_FILENAME} !-f
RewriteRule ^([^\.]+)$ $1.php [NC,L]