Hello,
I know the mixed content problem is a common problem here, however this is a special case.
I am using CloudFlare’s flexible SSL. This means CloudFlare provides the SSL for me but it passes non-ssl requests to my server. This means plugins like wp force ssl won’t help either. I simply don’t understand why your theme links images with the absolute URL instead of using relative URL paths like ‘/wp-content/uploads/xy.png’, that’s absolutely pointless exactly because of conflicts like this one.
I was able to fix the header images by changing the path from a full URL to the relative url. However I am not sure how I could achieve the same for all images in my image library.
In the private content field there are some examples of requests which are considered as mixed content.
Fixed it by switching to Full SSL and using the Really Simple SSL plugin