I have a photo of one of the ChäsExpress vehicles approaching Bern on
the Aare bridge. It is the 2nd vehicle in the train. First vehicle is a
Russian sleeping car. Other coaches in the train are all EWIV type. It
was taken in September 1992, when I think the Russian vehicle only went
as far as Bern (but it may have been Lausanne).
Unfortunately, this doesn't really answer your original question. Yes,
with the Russian sleeper, it could be described as an international
train, but it's more likely to be an internal train with the Russian
coach added as a through vehicle.