Hi Mary,
Thanks for the reply!
Forgive me, it might have been how I explained it, but I don't think this is related to the text editors.
The HTML block has the additional setting for CSS classes that are applied to the blocks div element, so I'm not referring to the content of the block itself, but it's general markup.
In boost/classes/output/core_renderer.php the block context is put together around line 330 in the 'block' function and doesn't appear to include the classes as set by each block type. I guess I was looking for something along the lines of $context->classes = $bc->attributes['class']; ??
This would then need to be rendered in the block.mustache template file as {{classes}} if my understanding is correct. By default, the block's class is set and the type is taken from the context as block_{{type}}.
Anthony