Broken urls with http site and https wp-admin

I am currently using a wordpress installation in which all the website is intended to be shown in http while the https part is protected by a self signed certificate, distributed manually to the admins. The problem I have is that the images uploaded are all uploaded with the “https” prefix, I imagine because the link is generated somehow using the full path of the admin interface.
Do you know how I can fix this behaviour to use the protocol http for every image uploaded? I don’t really need https for this and the site name and URL is in http.

Thanks in advance.

Some specs:

• wordpress version: 4.2.1
• plugins installed: Category Posts Widget, Jetpack, Post Types Order, Relative Image URLs, WordPress SEO, WP Statistics.

My advice is to make the whole site https. Either add https to the settings -> wordpress address & settings -> site address or remove https if it appears in either of those inputs.

For securing admin login panel only:

1. easy method but doesn’t show secure icon.
2. right result but more steps to consider method.