multi-vocab filter + show child term's nodes

I have been searching for a way to display nodes filtered by terms from more than one vocabularly, plus any nodes belonging to child terms. I can get the desired result by manually entering a URL such as /taxonomy/term/3+16. It would need a form containing several drop-down lists (one for each required vocab) which then displayed the appropriate nodes.

Is there a module already that does this?
Is there another approach that will do this?
Should I develop a module to do this?
Maybe the views module will do this but I haven't found the clue yet?

I have looked at category, directory and taxonomy_menu modules. They all show a hierarchical menu, but if a category (term) is selected that has no postings, nothing is displayed. I want to see any postings belonging to child terms of the selected term.
Taxonomy_browser comes close but does not show nodes belonging to child terms.

Have also checked some code snippets.

So there are two issues, multiple vocabs and dealing with child terms.

Hope this makes some sense.