Thunderbird HTML editor. This add-on adds a HTML tab to the composition window where you can see and edit the HTML source of the message.
This add-on is free software. However, after a while it will request to make a donation. People who have paid the minimum suggested contribution (US$ 5.99) will receive a license code to stop further reminders.
Original idea by Łukasz 'Arivald' Płomiński, author of the Stationery add-on.
Based on Ace HTML editor, https://ace.c9.io/.
HTML icon by PelFusion (www.pelfusion.com).
Note: I liked the font preview in the font indicator that 'Stationery' provides. So I included it here, too.
For Thunderbird 60.0 please visit the "All Versions" section to download a compatible version.
If the HTML tab doesn't work for you, that is, the insertion position doesn't coincide with the caret position, make sure you have a monospace font selected for monospace in "Fonts & Encodings" and that you don't set fonts in your userChrome.css without also adding this line: