'Alternativ' may be the closest, it's certainly similar and probably often overlaps.
However, the word 'alternative' could also be used for small publications in English, and to me it suggests a slightly different emphasis than 'progressive,' which seems more specifically political, or at least socially activist.
For me, alternative media is more associated with youth or young-adult culture, unlike traditional newspapers and magazines. In format, it could be the latest internet technology -- think blogs, video-exchange websites, online-only publications, online chats with reporters, and so on -- or a free local weekly tabloid-size newspaper of the kind found in many large US cities. In content, it could be not even reporting or analyzing the news in a traditional sense but focusing more on style or entertainment outside mainstream culture -- the alternative music scene, the latest tattoos & piercings, cable-only comedy shows, etc.
But again, I don't know to what extent these cognates may be semi-false friends; if 'alternativ' doesn't connote all that in German, it may be fine.