Avoid "Only Display Secure Content is Displayed" in IE with YouTube embeds

I recently set up a Drupal site that's all https, but IE (like I figured it would) doesn't like my YouTube embeds (and it also doesn't like my Twitter timeline box). Is there anything I can do on my end to stop this message from being displayed? It pops up on EVERY page (I think it's hitting our ads on the other pages).

What's odd is, my embeds have the https:// in the link. I can deal with the Twitter box, but YouTube embeds are a lot of the content on the site and are important.

I tried searching, but all I can really find is how to fix it on the user end.