I have installed Facebook like, share and comment buttons on my website and most of functionalities seem to be working ok, but after sharing a page on Facebook, thumbnail shows a blank page (clicking thumbnail takes user to the shared page, so there's no problem with that). Apparently this is how Facebook scraper sees my whole website.
I have determined that the probable cause is that the scraper (for some reason unknown to me) looks for website files in /var/www directory of my server, while website is located at /var/www/websitename/web. I have no idea what causes this, nor was I able to somehow direct Facebook scraper to correct path. What can I do to make everything work properly? I am using Debian+Apache+ISPConfig, website runs on Joomla!.
And the problem is solved. It was not SSL issue, nor any bug with code on my site. The problem was with Apache virtual host being configured for xx.xx.xx.xx:80 and xx.xx.xx.xx:443. Changing that to *:80 and *:443 automagically solved every problem Facebook scraper ever listed. Leaving this answer in case someone ever needs it.