I use this combination too, and I love it. Sphinx has great hackability and support, while github pages is free and very reliable. Here is a script that I use to publish to github pages, assuming the sphinx config is under "docs":

     sphinx-build docs docs/html
     git branch -D gh-pages || true
     git checkout -B gh-pages-stage
     touch docs/html/.nojekyll
     git add --force docs/html
     git commit -m "Docs"
     git push --force origin $(git subtree split --prefix docs/html --branch gh-pages):refs/heads/gh-pages
     git checkout -