I'm hoping to use Deepdwn with Nikola, which is a static site generator written in Python. This allows the use of Python-Markdown Extra which is similar to PHP Markdown Extra.
Using either of those extensions allows the following code to interpret the markdown and HTML correctly:-
<SECTION markdown="1"> ## A level two heading A paragraph with **bold** and *italics*. </SECTION>
It looks like you have to jump through a few more hoops to do something similar in CommonMark.
Edit: Hmm. This site seems to remove the blank line between the heading and the paragraph. Imagine there is one there.