By default when you publish to web, Animate points to a hosted version of its runtime file, as well as jQuery.
However, you can overrride this setting by going to File > Publish Settings > Web and then unchecking "Host runtime files on Adobe CDN". Publish to web again and you'll get an edge_includes folder as well as all the other published files. Upload all these files to your server and I think that will solve your mixed content warnings.
That worked great! Thanks for you help Joe.
I'm working on large project that will contain many Adobe Edge Animate created packages. The project is being deployed on secure site and requires all assets to be from secure sites. I'd rather not publish the runtime with every Adobe Edge Animate package. After a bit of poking around, it looks like the URLs in the edgePreload.js files can all be changed to https (instead of http) except the http://download.adobe.com/pub/adobe/edge/animate/2.0.1/edge.2.0.1.min.js file. Is there a publically hosted version on a secure site somewhere of this?
Quick update ... this has been resolve in Adobe Edge Animate 3.0 (released in Jan '14). There is no need to alter the "published" package.