We have national media (German: srf, French/Italian: rts, Romanche: rtr), people consume that, and a few medias that have multiple language versions like 20minutes.
We also have a few language specific medias (German: NZZ, Tagesanzeiger, Blick, ..., French: Le Temps, 24 heures, La Liberté, ...), but I think most people consume Swiss media, especially when Swiss politics and local afairs are absolutely not covered by French and German medias.