Images break with https:// prefix

When my website or blog post is accessed with the https:// prefix, images will not display. When the prefix is left off or http:// is used, images show up just fine. I searched forums and found a solution (copied in below), but that solution now appears to be invalid as” Full URL path to files” is no longer an option. How can I fix this?

Here’s an example post:

Broken: https://www.merriman.com/investing-101/should-your-home-be-considered-in-your-asset-allocation/

Works: http://www.merriman.com/investing-101/should-your-home-be-considered-in-your-asset-allocation/

Settings > Media > Full URL path to files

and changed the URL so that it uses the domain for the SSL host. I then updated the HEADER_URL in my theme’s functions.php file. Finally, I used the Search and Replace plugin to safely update existing image URLs in the post_content and guid fields of the _posts table and the meta_value field of the _postmeta table.