We haven't implemented it yet, but it is an important feature that we will implement: you will be able to download all your content as a .zip file containing OurBigBook Markup files, and then you will be able to generate the HTML for your content on your own computer with the open source OurB implementation. There are then several alternative ways to host the generated HTML files, including free ones such as GitHub Pages.
OurBigBook Docs
OurBigBook.comSite
Source code