You should use django-pjax which is built exactly for that kind of thing.
All you will have to do is to, in the base template, include the whole page or just the block contentbased on whether the request is ajax or not.
django-pjax does the AJAX calls using the jQuery and manipulates history using HTML5 push state API, which is a very good way to do it and also gracefully degrades in IE older versions.