How to set HTTP request headers for WebView requests?

Question

I am creating a hybrid application with Cordova 4 that interacts with a custom backend over HTTP. The backend authenticates each HTTP request using basic HTTP authentication.

Enabling HTTP basic authentication headers is easy for AJAX requests, but how do you set the headers for requests triggered by the DHTML application that are automatically launched by the WebView platform component? WebView doesn't seem to handle Basic authenification automatically if the server requires it.