FWIW: calibre companion is a native android app and it uses digest authentication and ajax. All we needed to do was set up the correct security environment in the http connection.
Code:
// Set up authentication. Try digest before basic
List<String> authpref = new ArrayList<String>();
authpref.add(AuthPolicy.DIGEST);
authpref.add(AuthPolicy.BASIC);
httpClient.getParams().setParameter(AuthPNames.TARGET_AUTH_PREF, authpref);
Of course, if you do not have access to the underlying http connection then this scheme will not work.