Elie -
Actually, the diglossia gets even worse when you delve a little more deeply. There are Swiss who have a dialect that is by family heritage (say, because their family comes from Kt. Bern), but then they moved (say, to Basel or the Aargau) and therefore speak the local dialect - and *then* the kids go to school and have to speak High German.

But I'd agree with a number of the other posts about the impossibility of a 'high' Swiss-German. Actually, about 20 years ago there was a big debate about the flattening of regional dialects because so much of what people were hearing on radio and TV was Zürich dialect. So there was a backlash, one that went along with de-monopolizing the airwaves, with the result that you not only have a lot of regional radio programs (in the relevant dialect) but that you have more diversity among those who are announcers on the national TV channels (including some lovely Walliser and Bündner - who themselves have to make an effort to *not* use some of their favorite words and expressions because other dialect speakers won't understand...
In print as well - esp. odd because Swiss-German is not a written dialect/language - there has been a big upsurge in publications, some of which is almost impossible to read unless you try to sound out the words and figure out what the author might have meant.

Bottom line (and tough on non-Swiss): dialect diversity has become more prominent in the media than it used to be...

J.