You're missing a bit. Try this; it's from some of my code:

You need to register the Umbraco controllers and the UmbracoContext.

    public static ContainerBuilder GetContainerBuilder(params Assembly[] controllerAssemblies)
    {
        // IoC setup
        var builder = new ContainerBuilder();

        // Register Umbraco Context, MVC Controllers and API Controllers.
        var umbracoAssembly = typeof(UmbracoApplication).Assembly;
        builder.Register(c => UmbracoContext.Current).AsSelf();
        builder.RegisterControllers(umbracoAssembly);
        builder.RegisterApiControllers(umbracoAssembly);

        var currentAssembly = typeof(DependencyInjectionConfig).Assembly;
        builder.RegisterControllers(currentAssembly);
        builder.RegisterApiControllers(currentAssembly);

        if (controllerAssemblies != null && controllerAssemblies.Any())
        {
            builder.RegisterControllers(controllerAssemblies);
            builder.RegisterApiControllers(controllerAssemblies);
        }
        // Register the types we need to resolve with Autofac here

        // Set Resolvers
        var container = builder.Build();
        System.Web.Mvc.DependancyResolver.SetResolver(new AutofacDependencyResolver(container));
        System.Web.Http.GlobalConfiguration.Configuration.DependancyResolver = new AutofacWebApiDependencyResolver(container);

        return builder;
    }