Unity Application Block, inherited injection

class Program
{
    static void Main(string[] args)
    {
        UniversalComposition universe = new UniversalComposition();


    }
}

public class UniversalComposition : Composition
{
    // Everything that gets resolved in this container should contain a child container created by the this container

    public UniversalComposition()
    {
        this.Container.RegisterType<IService, Service>();
    }

    protected override IUnityContainer CreateContainer()
    {
        return new UnityContainer();
    }

}

public abstract class Composition
{
    protected IUnityContainer Container {get; private set;}

    public Composition()
    {
        this.Container = this.CreateContainer();
    }

    public TInstance Resolve<TInstance>()
    {
        return this.Container.Resolve<TInstance>();
    }

    protected abstract IUnityContainer CreateContainer();
}

public class Service : Composition, IService
{
    public Service(/* I want to inject a child Unity Container in here container.CreateChildContainer() */)
    {
    }
}

public interface IService { }

public abstract class BaseClass
{
    public IUnityContainer Container { get; protected set; }

    public BaseClass() : BaseClass(null) {}

    public BaseClass( IUnityContainer container )
    {
        this.container = container ?? this.CreateContainer();
    }

    public abstract IUnityContainer CreateContainer();
}

public class DerivedClass : BaseClass
{
    public IUnityContainer ChildContainer { get; private set; }

    public DerivedClass() : DerivedClass(null,null) {}

    public DerivedClass( IUnityContainer parent, IUnityContainer child )
        : BaseClass( parent )
    {
        this.ChildContainer = child ?? this.CreateChildContainer();
    }

    public IUnityContainer CreateContainer()
    {
         return new UnityContainer();
    }

    public IUnityContainer CreateChildContainer()
    {
         return this.Container.CreateChildContainer();
    }

}