When you share a post on Facebook, or when Jetpack Publicize publishes a post to your Facebook page, Facebook crawls the page and looks for Open Graph meta tags in the head to build a complete post preview (with an image, title, description, …).
Jetpack builds these meta tags for you, unless you already use another plugin to do so. On your site, Open Graph meta tags are managed by the WordPress SEO plugin.
However, your theme or one of your plugins seem to force WordPress to generate relative URLS instead of the default absolute URLs. As a result, Facebook and Twitter cannot gather any relevant information about your post.