The depth filter on views taxonomy view is not only capable of allowing multiple terms through comma or plus signs, but it is capable of using a depth modifier. If I set the depth modifier to '1' then all children will show whenever I am on the parent term's page, even though the children aren't actually tagged with the parent term. However, Taxonomy Filter does not account for this and the facets are removed from the page since it doesn't recognize the child terms when filtering.

Example:
I have a hierarchy of:
Series 1 (Desert Card)
- Mainline

Parent
http://pixarcarsdiecastwiki.com/series/series-1-desert-card
notice the empty refine your search on the right-hand side.

Child
http://pixarcarsdiecastwiki.com/series/series-1-desert-card/mainline
notice the refine your search now appears

All the nodes in those pages are tagged with the child term Mainline. They are not however tagged with the parent Series 1 (Desert Card).

I have that taxonomy page rendering through views with Multi-term views and a patch to fix the D7 problem with views depth parameter not working in Multi-term views.