URL Routing Rewrite Path But Keep Mimetype?

I have implemented my own IRouteHandler for URL routing. For files without extension it will try to load the filename as a Page from the Pages directory with:

return (IHttpHandler) BuildManager.CreateInstanceFromVirtualPath(path, typeof(Page));

However there are also images and css files (with relative paths) that need to be translated to the correct url. I try to service those files with:

try {
HttpContext.Current.Server.Transfer(fileName);
} catch (HttpException) {
throw new HttpException(404, "file not found");
}

This works fine (in Internet Explorer), however Firefox is giving me an error:

Styles.css was not loaded because its MIME type, "text/html", is not "text/css".

Is this caused by the Server.Transfer? What should I use to redirect the file? Response.Redirect is visible to the client.