How can I run both HTML linting and CSS linting when using mode: htmlmixed?

I’m trying to run both HTMLHint and CSSLint on a CodeMirror instance that has mode: "htmlmixed" . Is this not supported or is there some extra work I need to do to get it activated? I’ve switched the mode to css and can confirm that the CSS Linting scripts are loaded properly. The Linter demos here (https://codemirror.net/demo/lint.html) don’t show this capability but I was hoping it existed.

As an example, the HTMLHint website at https://htmlhint.io/ supports running CSSLint simultaneously. But they are using the Ace Code Editor and not CodeMirror.

My apologies if this isn’t the right place to ask this question!