onMouseOver, onMouseOut and <div>

I have to make a dynamic menu in javascript, so I use onMouseOver and onMouseOut, but the problem is when I focus my mouse on line space, the menu dissapear because it think I'm no more in the div!

<script type="text/javascript">
function cacherSousMenu(menu)
{
    if(menu == "ajout")
    {
        document.getElementById('sousMenuAjout').style.display = document.getElementById('sousMenuAjout').style.display=='none'?'block':'none';
        document.getElementById('imgPlusMoinsAjout').src = document.getElementById('sousMenuAjout').style.display=='none'?'images/plus.gif':'images/moins.gif';
    }
    else if(menu == "inscrire")
    {
        document.getElementById('sousMenuInscrire').style.display = document.getElementById('sousMenuInscrire').style.display=='none'?'block':'none';
        document.getElementById('imgPlusMoinsInscrire').src = document.getElementById('sousMenuInscrire').style.display=='none'?'images/plus.gif':'images/moins.gif';
    }
}

<nav>
<ul>
<div id="ajouter" onmouseover="cacherSousMenu('ajout');">
<li class="titre">Ajouter <img src="images/plus.gif" id="imgPlusMoinsAjout" alt="Image Plus Moins"></li>
</div>
<div id="sousMenuAjout" onmouseout="cacherSousMenu('ajout');">
<ul>
<li><a href="index.php?page=3">Un établissement</a></li>
<li><a href="index.php?page=4">Une filière</a></li>
<li><a href="index.php?page=5">Une UE</a></li>
</ul>
</div>
<div id="inscrire" onmouseover="cacherSousMenu('inscrire');">
<li class="titre">Inscrire <img src="images/plus.gif" id="imgPlusMoinsInscrire" alt="Image Plus Moins"></li>
</div>
<div id="sousMenuInscrire" onmouseout="cacherSousMenu('inscrire');">
<ul>
<li><a href="index.php?page=2">Un nouvel étudiant</a></li>
<li><a href="index.php?page=6">Un étudiant à une UE</a></li>
</ul>
</div>
<li class="titre"><a href="index.php?page=7">Afficher tous les étudiants</a></li>
<li class="titre">Aide</li>
<ul>
</nav>

So, how to correct that, maybe with CSS?

Thank!

Solution

I can't help but wonder if you should post a question (or look for one) on https://ux.stackexchange.com/ about menu behaviour, and in particular, hover states (which don't exist on pads and phones which are becoming more prolific). But to solve your technical issue...

It takes a lot more than just mouse over and mouse out to make a menu behave nicely. Most good menus allow a grace period for user error, meaning the mouse can leave the menu briefly. Again, to simply solve your technical issue of the menu flashing when you move your mouse:

You have DIVs and list items mixed up a little. I've added some bright colours to help clarify the elements, and converted the DIVs to list items for simplicity. I also refactored your JavaScript method to make it slightly less tightly coupled with your markup. I hope you find it useful.

<!doctype HTML>
<html>
<head>
<style>
.titre {background-color:red;}
.menuItemWrapper {background-color:green;}
</style>
</head>
<body>
<nav>
    <ul id="ajouter" onmouseover="showMenu('sousMenuAjout','imgPlusMoinsAjout',true);" onMouseOut="showMenu('sousMenuAjout','imgPlusMoinsAjout',false);">
            <li class="titre">Ajouter <img src="images/plus.gif" id="imgPlusMoinsAjout" alt="Image Plus Moins"></li>
        <ul id="sousMenuAjout" class="menuItemWrapper" onMouseOut="hideMenu('sousMenuAjout');">
                <li><a href="index.php?page=3">Un établissement</a></li>
                <li><a href="index.php?page=4">Une filière</a></li>
                <li><a href="index.php?page=5">Une UE</a></li>
            </ul>
    </ul>

    <ul id="inscrire" onmouseover="showMenu('sousMenuInscrire','imgPlusMoinsInscrire',true);" onMouseOut="showMenu('sousMenuInscrire','imgPlusMoinsInscrire',false);">
        <li class="titre">Inscrire <img src="images/plus.gif" id="imgPlusMoinsInscrire" alt="Image Plus Moins"></li>
        <ul id="sousMenuInscrire" onmouseout="cacherSousMenu('inscrire');" class="menuItemWrapper">
            <ul>
                <li><a href="index.php?page=2">Un nouvel étudiant</a></li>
                <li><a href="index.php?page=6">Un étudiant à une UE</a></li>
            </ul>
        </ul>
        <li class="titre"><a href="index.php?page=7">Afficher tous les étudiants</a></li>
        <li class="titre">Aide</li>
    </ul>
</nav>
<script type="text/javascript">
function showMenu(menuId, menuIconId, visible) {
    var displayStyle, imageName;
    if (visible) {
        displayStyle = 'block';
        imageName = 'images/moins.gif';
    } else {
        displayStyle = 'none';
        imageName = 'images/plus.gif';
    }
    document.getElementById(menuId).style.display = displayStyle;
    document.getElementById(menuIconId).src = imageName;
}
showMenu('sousMenuAjout', 'imgPlusMoinsAjout', false);
showMenu('sousMenuInscrire', 'imgPlusMoinsInscrire', false);
</script>
</body>
</html>

You can see this live on jsbin (doesn't work in jsFiddle for some reason): http://jsbin.com/exakiz/2

PS. Sorry I switched some names to English; I don't speak or understand French. :(