Thanks Jan but the behavior appears to be controlled through some additional JavaScript as well. The text field that contains the URL appears to also have a JS 'onblur' event that changes the URL protocol to http immediately.
We've been searching through the code but haven't found the file yet. If you could point us in the right direction that would be much appreciated.
[update]
When looking at the developer console in Chrome, the mixed mode warning I receive is on this page: /CMSFormControls/Selectors/InsertYouTubeVideo/Content.aspx. I believe this page is presented in the Admin overlay when adding a YouTube video.