When your Internet Explorer thinks that all files you download contain viruses, you have a problem. There are many posts about this all over the internet explaining the most complicated things.
In my case, it was actually very easy: IE is not to blame, it was SCEP (System Center Endpoint Protection) - also known as your anti-virus.
The resolution: uninstall SCEP, check with an online virusscanner (that you can find using your favorite Search Engine such as Bing) that you don't have rootkits or other viruses, and install SCEP again. Done.