You can use notmuch-show-view-part (bound to .-v by default) while point is in the text/html part to accomplish this.
For this to function properly you'll need to make sure your ~/.mailcap file has settings for text/html.
Here's what I have in mine on my Mac:
text/html; open %s; nametemplate=%s.html
Each line is ; delimited with the first field specifying ...