WordPress.com does not offer a way to edit theme HTML or PHP, so you cannot add new things below the header. However, what you can do is reposition other elements from the page. One example would be to reposition some footer image widgets. Another (simpler) option would be to create an already sized banner image and upload it to your media library and then add it below the site header as a background image using CSS. Or, if you wanted to pull the images just in one specific post, like the one you linked, to the top of the page, then I would recommend adding them to the top of the post first (instead of interspersed in the text like they are now) and then use CSS to move them above the post title.
I guess I'm not exactly sure which images you mean or if you wanted something different for different posts or if you just wanted to add a header background image different than the balloons. Could you reply back with a bit more detail?