Yes, thanks to all for the contributions.
Fortunately I'm in control of the HTTPS server side so I could fix the SSL certificate there by recreating it with the keytool options

-ext nas=ip:X.Y.Z.W,dns:localhost,dns:demohost

This adds a section like this

SubjectAlternativeName [
  DNSName: localhost
  DNSName: demohost
  IPAddress: X.Y.Z.W
]

into the certificate stored on the created server's keystore (jks). I then imported it (always with keytool) into the cacerts of the jdk I use to run basex with. Finally I restarted basex server and gui. At that point everything works fine and I can send-request to either of the three possibilities ('localhost', ip address or any other added dns name like 'demohost').

I know this is not basex specific but maybe this detailed answer could be useful for anyone who will stumble upon this discussion for the same reasons as mines.

Thanks again,
Marco.

On 02/06/2014 02:59 PM, Florent Georges wrote: