JQuery :: Building Unordred List - Using DIV With UL

I want to construct HTML for a menu and I want to use DIV with UL. The data for the link and text would be coming from a web service which is a sharepoint list like so. As you can see below I want to grab the rows and and it to anchor links...
$(document).ready(function() {
$().SPServices({
operation: "GetListItems",
async: false,
listName: "MenuList",
CAMLViewFields: "<ViewFields><FieldRef Name='Title' /></ViewFields>",
completefunc: function (xData, Status) {
$(xData.responseXML).find("[nodeName=z:row]").each(function() {
var liHtml = $(this).attr("ows_Title") ; $("#mainmenu").append(liHtml);
});
}});
});

The desired HTML would look like so
<div id="mainmenu">
<div id="header">
<ul id="navbar">
<li class="menu"><a href="#">Home</a>
<ul>
<li><a href="#">liHtml </a></li>
<!--I want to keep adding the <li> element with new item-->
<li><a href="#">Menu item 2</a></li>
<li><a href="#">Menu item 3</a></li>
<li><a href="#">Menu item 4</a></li>
<li><a href="#">Menu item 5</a></li>
</ul></li>
</ul></div>
</div>