Using jquery to show xml tree view

I have a doubt about my application. I have created an xml tree using jquery and I have a checkbox on my tree view.

For that when I tick my parent node then the entire sub child also get ticked and this is okay

When i untick my parent node then the entire sub child also unticked and this is also okay

But when I do 1. and then I untick all the subchilds then I want my parent node also untick automatically, but this is not happen in my code

Let me know if i have done anything wrong. Here is my code:

HTML
 

<div>
    <style type="text/css">
        ul
        {
            margin-left: 0px;
            list-style: none;
            padding-left: 40px;
            margin-left: -20px;
            padding: 0 0 0 16px;
            margin: 0;
        }
        li
        {
            margin: 0;
            padding: 0px 0 5px;
        }
    </style>
    <script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/1.8.3/jquery.min.js"></script>
    <script type="text/javascript">
        $(function () {
            var xmlData = readXml('<%= ResolveUrl("~/XmlFiles/XMLFile.xml") %>');
            var sHTML = drawTreeFromXml(xmlData);
            document.getElementById("tree").innerHTML = sHTML;
        });
 
        function drawTreeFromXml(xmlData) {
            var html = "";
            var properties = xmlData.getElementsByTagName("properties");
            html += ""
            $(properties).each(function () {
                var department = $(this);
                var CustomerID = $(department).find("CustomerID").text();
                html += "<ul>";
                html += "<li><input type='checkbox'/><a href='javascript:;'>" + CustomerID + "</a>";
                html += "<ul>";
                var CompanyName = $(department).find("CompanyName").text();
                html += createElement(CompanyName);
                var ContactName = $(department).find("ContactName").text();
                html += createElement(ContactName);
                var ContactTitle = $(department).find("ContactTitle").text();
                html += createElement(ContactTitle);
                var Address = $(department).find("Address").text();
                html += createElement(Address);
                var City = $(department).find("City").text();
                html += createElement(City);
                var PostalCode = $(department).find("PostalCode").text();
                html += createElement(PostalCode);
                var Country = $(department).find("Country").text();
                html += createElement(Country);
                var Phone = $(department).find("Phone").text();
                html += createElement(Country);
                var Fax = $(department).find("Fax").text();
                html += createElement(Fax);
                html += "</ul></li></ul>";
            });
            return html;
        }
 
        function createElement(ElementValue) {
            return "<li><input type='checkbox'/><a href='javascript:;'>" + ElementValue + "</a></li>";
        }
        $("#tree input:checkbox").live('change', function () {
            if ($(this).nextAll('ul').length == 0) {
                if ($(this)[0].checked == false) {
                    $(this).closest('ul').parent().find('input:checkbox').eq(0).attr('checked', false);
                } else {
                    if ($(this).closest('ul').parent().find('input:checkbox:checked').length == $(this).closest('ul').parent().find('input:checkbox').length - 1) {
                        $(this).closest('ul').parent().find('input:checkbox').eq(0).attr('checked', true);
                    }
                }
            } else {
                if ($(this)[0].checked == true) {
                    $(this).nextAll('ul').find('input:checkbox').attr('checked', true);
                } else {
                    $(this).nextAll('ul').find('input:checkbox').attr('checked', false);
                }
            }
        });
 
 
        $('#tree a').live('click', function () {
            if ($(this).nextAll('ul').length != 0) {
                if ($(this).nextAll('ul').is(':visible')) {
                    $(this).nextAll('ul').hide();
                } else {
                    $(this).nextAll('ul').show();
                }
            }
        });
 
 
        function readXml(xmlFile) {
            var xmlDoc;
            if (typeof window.DOMParser != "undefined") {
                xmlhttp = new XMLHttpRequest();
                xmlhttp.open("GET", xmlFile, false);
                if (xmlhttp.overrideMimeType) {
                    xmlhttp.overrideMimeType('text/xml');
                }
                xmlhttp.send();
                xmlDoc = xmlhttp.responseXML;
            }
            else {
                xmlDoc = new ActiveXObject("Microsoft.XMLDOM");
                xmlDoc.async = "false";
                xmlDoc.load(xmlFile);
            }
            return xmlDoc;
        }      
    </script>
    <div id="tree">
    </div>
</div>

XMLFILE.xml:
 
<?xml version="1.0" encoding="utf-8" standalone="yes"?>
<feed>
  <entry>
    <content>
      <properties>
        <CustomerID>ALFKI</CustomerID>
        <CompanyName>Alfreds Futterkiste</CompanyName>
        <ContactName>Maria Anders</ContactName>
        <ContactTitle>Sales Representative</ContactTitle>
        <Address>Obere Str. 57</Address>
        <City>Berlin</City>
        <PostalCode>12209</PostalCode>
        <Country>Germany</Country>
        <Phone>030-0074321</Phone>
        <Fax>030-0076545</Fax>
      </properties>
    </content>
  </entry>
  <entry>
    <content>
      <properties>
        <CustomerID>ANATR</CustomerID>
        <CompanyName>Ana Trujillo Emparedados y helados</CompanyName>
        <ContactName>Ana Trujillo</ContactName>
        <ContactTitle>Owner</ContactTitle>
        <Address>Avda. de la Constitución 2222</Address>
        <City>México D.F.</City>
        <PostalCode>05021</PostalCode>
        <Country>Mexico</Country>
        <Phone>(5) 555-4729</Phone>
        <Fax>(5) 555-3745</Fax>
      </properties>
    </content>
  </entry>
</feed>