I tested two ways:
1. create an html page that contains img tags with src to fully-qualified https urls on the same site, and then access via http. For example, create test-page-1.html:
...some html...
>img src="https://mysite.foobar.com/image.gif">
...some html...
some more image tags with https references
...more html..
then reference the page from the browser:
http://mysite.foobar.com/test-page-1.html
2. create an html page that contains img tags with src to fully-qualified http urls on the same site, and then access via https. For example, create test-page-2.html:
..some html..
>img src="http://mysite.foobar.com/image.gif">
..some html..
some more image tags with http references
..more html..
then reference the page from the browser:
https://mysite.foobar.com/test-page-2.html
Note: Request the page using the http/https protocol *not* used in the image references.