This cognitive bias does not have a description yet.
The hostile media effect is the tendency for people who have taken a position on an issue to see media coverage of that issue as biased against their position.
For example, in the first study done on the topic, a number of subjects watched news clips of the coverage of a massacre of Palestinian refugees by a Lebanese militia during the Lebanese Civil War. The pro-Israeli subjects were more likely to think that the coverage had a pro-Palestinian bias while the pro-Palestinian subjects thought the opposite. This concept probably explains many of the accusations of liberal/"corporate"/Zionist/FSM-biased media. In short, it's impossible for media to be unbiased when you, yourself, have a bias.