If you're using jQuery you can also use the "mouseleave" function, which deals with all of this for you.
$('#thetargetdiv').mouseenter(do_something);
$('#thetargetdiv').mouseleave(do_something_else);
do_something will fire when the mouse enters thetargetdiv or any of its children, do_something_else will only fire when the mouse leaves thetargetdiv and any of its children.