Use Better Jinja together with HTMLHint?

Question

I've been using Better Jinja in a project to get syntax highlighting of Jinja code inside of HTML files. I associated all html files with Better Jinja like this:

"files.associations": {
    "*.html": "jinja-html"
}

Now I wanted to add HTMLHint to the same project but somehow I get no hints in my HTML files. I added these associations for HTMLHint: (the last one is just a guess on my side since the first two didn't seem to work)

"htmlhint.documentSelector": [
    "html",
    "htm",
    "jinja-html"
]

But this seems to have no effect. If I switch the file type in the status bar from "Jinja HTML" to "HTML" then HTMLHint starts working but I lose all the Jinja highlighting.

Is there a way to have both extensions working together?