After some more googling, and experimenting I found out, that you have to define IIS settings in the Web.config
.
After adding the following configuration:
<system.webServer>
<staticContent>
<mimeMap fileExtension=".json" mimeType="application/json" />
</staticContent>
</system.webServer>
it works like a charm.
Full setup file example:
<?xml version="1.0"?>
<configuration>
<system.web>
<compilation debug="true" targetFramework="4.0"/>
</system.web>
<system.webServer>
<staticContent>
<mimeMap fileExtension=".json" mimeType="application/json" />
</staticContent>
</system.webServer>
</configuration>