Update your script as follows :
<script type="text/javascript">
$(function () {
$(".sub").hide();
$("#btnHomeLi").mouseenter(function () {
$(".sub").slideDown('slow');
});
$("#btnHomeLi").mouseleave(function () {
$(".sub").slideUp('slow');
});
$('.sub').hover(function () { $(this).stop(); }, function () { $(this).slideUp('slow'); });
});
</script>