The probem I have is that I can click on the calendar "attachement" (which is reckognized as this) but nothing happens then ...

I guess the problem is caused by the invitation not being an attachment but an inline VCALENDAR entry...
I tried now at home with Thunderbird/Lightening and Outlook at work

BEGIN:VCALENDAR
PRODID:-//Mozilla.org/NONSGML Mozilla Calendar V1.1//EN
VERSION:2.0
METHOD:REQUEST
BEGIN:VTIMEZONE
TZID:Europe/Berlin
X-LIC-LOCATION:Europe/Berlin
BEGINAYLIGHT
TZOFFSETFROM:+0100
TZOFFSETTO:+0200
TZNAME:CEST
DTSTART:19700329T020000
RRULE:FREQ=YEARLY;BYDAY=-1SU;BYMONTH=3
ENDAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0200
TZOFFSETTO:+0100
TZNAME:CET
DTSTART:19701025T030000
RRULE:FREQ=YEARLY;BYDAY=-1SU;BYMONTH=10
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CREATED:20130214T184716Z
LAST-MODIFIED:20130214T184750Z
DTSTAMP:20130214T184750Z
UID:85447822-3273-4dc1-a49a-38a800a3391a
SUMMARY:Neuer Termin
ORGANIZER;RSVP=TRUE;CN=ME;PARTSTAT=ACCEPTED;ROLE=C HAIR:mailto
rganiser@mail.com
ATTENDEE;RSVP=TRUE;PARTSTAT=NEEDS-ACTION;ROLE=REQ-PARTICIPANT:mailtoarticipant@mail.com
CATEGORIES:Feiertag
DTSTART;TZID=Europe/Berlin:20130216T200000
DTEND;TZID=Europe/Berlin:20130216T210000
LOCATION:A test date
TRANSP:OPAQUE
CLASS:PUBLIC
END:VEVENT
END:VCALENDAR