I have this markdown code in a Markdown file. It has inline HTML.
---
layout: page
title: About This Website
permalink: /about/
---
This website is built w
That's exactly how the original Markdown implementation works:
Note that Markdown formatting syntax is not processed within block-level HTML tags. E.g., you can’t use Markdown-style
*emphasis*
inside an HTML block.
Jekyll uses Redcarpet by default which behaves the same way. If you are running Jekyll yourself you might be able to create a custom Markdown processor to do what you want, but that won't work if you're using something like GitHub Pages for hosting.