Links are wrongly https on http pages

Hi, I have a clean wordpress installation on https://www.iubenda.com/wordpress, which I set up for debugging purposes after experiencing this problem on https://www.iubenda.com/blog). What happens is that http pages, like the blog home page I linked, have links, canonical urls and part of the resources in https. Of course, I don’t want the blog to behave this way.

I also tried to set up a wordpress.iubenda.com, and there the problem does not happen. The only guess I was able to make is that there must be some configuration for the main / path three, which does have https (but still not default), that is wrongly interpreted by wordpress and causes this weird behavior.

Any clue on what could be happening and how to fix it? Do you think this might be a wordpress bug? Was SSL handling reworked recently in the codebase? (I also tried to install wordpress 3.4, and the result was the same, but I’ve not tried previous versions)

Thanks in advance.