Just FYI, after stumbling around for a fair while I found this web page: Deploying multiple virtual directories to a single Azure Website <http://blogs.msdn.com/b/tomholl/archive/2014/09/22/deploying-multiple-virtual-directories-to-a-single-azure-website.aspx> in which he deploys the main site to Azure, then creates a virtual directory in the portal, then deploys a different app into that virtual directory. You have to follow his pattern exactly, and I doubt I would have tried this combination myself as there are no clues that it's a valid thing to do.
I spent half an hour trying all sorts of tricks to apply a default document (index.aspx in my case) to the app in the virtual directory, but the site's portal settings are ineffective and so are attempts to use a <defaultDocument> element in the app's config. *Greg K* P.S. My tiny site and app seem to have burnt about $2 overnight despite the fact there were only about 40 requests in total, so that hints at an annual cost of several hundred dollars. That's pretty scary.
