Unparsed-text-available returns true for XML files, so

I've got a situation where I've got a number of files I need to transform.  I
don't know what kind of files they are going to be (they are anything from an
enumerated list of file types, but can be anything from .mdb to .sql to .xml
to .xls and so on).  So, I need to test the file type and then process them
accordingly.
I thought the way to do this was to have unparsed-text() handle unparsed text
and have document() handle everything else - by attaching the appropriate URI
Resolver.  Then, if unparsed-text-available() returns true, I can send the
file data to a named template to handle appropriately and if
document-available() returns true, I can send to a matched template to do what
it needs to do.
But, I've just discovered that unparsed-text-available() will return true for
xml files.  So, I don't know how to distinguish within my xslt which files are
unparsed and which ones aren't.
I could use some guidance here, please.