JQuery :: Hover (Top Level Menu) Not Working In Mozilla Firefox

I have implemented a jQuery hover top level menu & it is working fine in bothIE 7& 8. However, when I am executing the same code in Mozilla Firefox, it is not rendering hover effect at all. Also, I am adding a <span> using jQuery if JavaScript isn't enabled. This span is also not getting added in Mozilla.

Following is the code that I am using.
<script type="text/javascript" src="[URL]"></script>
<script>
$(document).ready(function(){
$("ul.subnav").parent().append("<span></span>");
$("ul.pnode li a").mouseover(function() { //When trigger is clicked...
//Following events are applied to the subnav itself (moving subnav up and down)
$(this).parent().find("ul.subnav").slideDown('fast').show(); //Drop down the subnav on click
$(this).parent().hover(function() {
}, function(){
$(this).parent().find("ul.subnav").slideUp('slow'); //When the mouse hovers out of the subnav, move it back up
});
//Following events are applied to the trigger (Hover events for the trigger)
}).hover(function() {
$(this).addClass("subhover"); //On hover over, add class "subhover"
}, function(){ //On Hover Out
$(this).removeClass("subhover"); //On hover out, remove class "subhover"
});
});
</script>

I came to know that IE & Mozilla see .parent differently.I have tried everything but not able to get this stuff working in Mozilla. I am using Firefox 3.5.5 version.