There’s a new git-remote-hg that provides native support:
Bridge support in Git for Mercurial and Bazaar
Just copy git-remote-hg to your $PATH, make it executable, and that’s it, no dependencies (other than Mercurial):
git clone hg::https://www.mercurial-scm.org/repo/hg/
You should be able to push and pull from it as if it was a native Git repository.
When you push new Git branches, Mercurial bookmarks will be created for them.
See the git-remote-hg wiki for more information.