How to force the admin-ajax.php file to load over HTTPS?

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If you are using Domain Mapping plugin doing this will quickly achieve exactly what you are asking for.

  1. Go to: YOURDOMAIN/wp-admin/tools.php?page=domainmapping

  2. Under: Excluded pages, check: Force SSL for all pages.

  3. Save and you’re done.

Your insecure mixed content error due to admin-ajax.php loading via http instead of via https should be gone after this.