Asp.Net MVC3 Razor - child items list not posting back from editor

Question

I'm trying to create a multi-level editor in MVC3. By multi-level I mean that I would like to be able to edit data for three levels of hierarchy (parent object, parent's child object and collection of sub-child objects). My model roughly looks like:

namespace MvcApplication1.Models
{
    public class Parent
    {
        public int Id { get; set; }
        public string Name { get; set; }
        public Child Child { get; set; }
    }

    public class Child
    {
        public int Id { get; set; }
        public string Name { get; set; }
        public IEnumerable<SubChild> SubChildren { get; set; }    
    }

    public class SubChild
    {
        public int Id { get; set; }
        public string Name { get; set; }
        private DateTime _date = DateTime.Now;
        public DateTime Date { get { return _date; } set { this._date = value; } }
    }
}

Since I want to display the whole hierarchy on one screen I created the following view model:

namespace MvcApplication1.Models.ViewModels
{
    public class ParentViewModel
    {
        public int Id { get; set; }
        public string Name { get; set; }
        public Child Child { get; set; }
        public IEnumerable<SubChild> SubChildren { get { return Child.SubChildren; } set { this.Child.SubChildren = value; } }
    }
}

and controller is looks like:

    public class ParentController : Controller
    {
        public ActionResult MultiLevelEdit(int id)
        {
            // Simulate data retrieval 
            Parent parent = new Parent { Id = 2 , Name = "P"};
            var child = new Child { Id = 3, Name = "Cild1" };
            List<SubChild> children = new List<SubChild>();
            children.Add(new SubChild { Id = 3, Name = "S1"});
            children.Add(new SubChild { Id = 5, Name = "S 22" });
            child.SubChildren = children;
            parent.Child = child;
            // Create view model
            ParentViewModel vm = new ParentViewModel() { Id = parent.Id, Name = parent.Name, Child = parent.Child, SubChildren = parent.Child.SubChildren };

            return View(vm);
        }

    }

view being rendered is:

@model MvcApplication1.Models.ViewModels.ParentViewModel

@using (Html.BeginForm()) {
    @Html.ValidationSummary(true)
    <fieldset>

    @Html.HiddenFor(model => model.Id)
    @Html.LabelFor(model => model.Name)
    @Html.EditorFor(model => model.Name)
    <hr />
    Child
    <br />
    @Html.EditorFor(model => model.Child)

    <hr />
    SubChild
    <br />
    @Html.EditorFor(model => model.SubChildren)


    <p>
            <input type="submit" value="Save" />
        </p>
    </fieldset>
}

I have created two editor templates in the Views\Shared\EditorTemplates :

ChildTemplate.cshtml

@model MvcApplication1.Models.Child

@{
    ViewBag.Title = "Child";
}

<h2>Child</h2>

@using (Html.BeginForm()) {
    @Html.ValidationSummary(true)
    <fieldset>
        <legend>Child</legend>

        @Html.HiddenFor(model => model.Id)

        <div class="editor-label">
            @Html.LabelFor(model => model.Name, "Child Name")
        </div>
        <div class="editor-field">
            @Html.EditorFor(model => model.Name)
            @Html.ValidationMessageFor(model => model.Name)
        </div>
    </fieldset>
}

and SubChildTemplate.cshtml

@model MvcApplication1.Models.SubChild

@using (Html.BeginForm()) {
    @Html.ValidationSummary(true)
    <fieldset>
        <legend>SubChild</legend>

        @Html.HiddenFor(model => model.Id)

        <div class="editor-label">
            @Html.LabelFor(model => model.Name)
        </div>
        <div class="editor-field">
            @Html.EditorFor(model => model.Name)
            @Html.ValidationMessageFor(model => model.Name)
        </div>

        <div class="editor-label">
            @Html.LabelFor(model => model.Date)
        </div>
        <div class="editor-field">
            @Html.EditorFor(model => model.Date)
            @Html.ValidationMessageFor(model => model.Date)
        </div>
    </fieldset>
}

Everything renders correctly, however when I try to save the changes the SubChildren collection is null. I tried two signatures of the edit method:

[HttpPost]
public ActionResult MultiLevelEdit(ParentViewModel parentVM)
{...

[HttpPost]
public ActionResult MultiLevelEdit(ParentViewModel parentVM, FormCollection collection)
{...

and there is no value in any of those.

Can anyone suggest What could be improved to make that work? Thanks a lot in advance.