HTTPS doesn't switch to HTTP on "home page"

Assuming "Switch back to http pages when there are no matches" is enabled, when viewing a https page, then going to the home page (or) logging out (which by default, redirects to the home page), weird things happen. For example, if logged in, it will render the home page as not being logged in. (I know an issue has been brought up on this before). In chrome, the URI is https, but all css and js URLs are called from http and subsequently chrome "blocks" the non-secure files, rendering the home page without a theme...

The workaround I have found, which rather surprisingly works quite well, is to set the to "https".

So, before, I had my base_url set to:

$base_url = 'http://www.mywebsite.com';  // NO trailing slash!

and simply changed it to:

$base_url = 'https://www.mywebsite.com';  // NO trailing slash!

By changing the $base_url to https, when viewing the home page, it will force everything as https along with one or two non-ssl subsequent page requests, until "whatever cache" (??) has time to update itself and properly redirect back to http.

Hope this helps others in a similar situation.