HttpModule EndRequest handler called twice

I am attempting to implement authentication for a REST service implemented in WCF and hosted on Azure. I am using HttpModule to handle the AuthenticationRequest, PostAuthenticationRequest and EndRequest events. If the Authorization header is missing or if the token contained therein is invalid, during EndRequest I am setting the StatusCode on the Response to 401. However, I have determined that EndRequest is called twice, and on the second call the response has already had headers set, causing the code which sets the StatusCode to throw an exception.

I added locks to Init() to ensure that the handler wasn't being registered twice; still ran twice. Init() also ran twice, indicating that two instances of the HttpModule were being created. However, using Set Object ID in the VS debugger seems to indicate that the requests are actually different requests. I've verified in Fiddler that there is only one request being issued to my service from the browser.

If I switch to using global.asax routing instead of depending on the WCF service host configuration, the handler is only called once and everything works fine.

If I add configuration to the system.web configuration section as well as the system.webServer configuration section in Web.config, the handler is only called once and everything works fine.

So I have mitigations, but I really dislike behavior I don't understand. Why does the handler get called twice?

Here is a minimal repro of the problem:

Web.config:

  <system.web>
    <compilation debug="true" targetFramework="4.0" />
    <!--<httpModules>
      <add name="AuthModule" type="TestWCFRole.AuthModule, TestWCFRole"/>
    </httpModules>-->
  </system.web>
  <system.serviceModel>
    <behaviors>
      <endpointBehaviors>
        <behavior name="WebBehavior">
          <webHttp/>
        </behavior>
      </endpoint