Implementor.cs

public class Implementor {
    private readonly IParentInterface _parent;

    public Implementor (IParentInterface parent) {
        _parent = parent;
    }

    public void DoWork () {
        // Do work with parent interface method
        _parent.ParentWork ();

        // Do work with child interface method
        ((IChildInterface) _parent).ChildWork ();
    }
}