Try This :
<!-- Category Archive Start -->
<ul class="catArchive">
<?php
$catQuery = $wpdb->get_results("SELECT * FROM $wpdb->terms AS wterms INNER JOIN $wpdb->term_taxonomy AS wtaxonomy ON ( wterms.term_id = wtaxonomy.term_id ) WHERE wtaxonomy.taxonomy = 'category' AND wtaxonomy.parent = 0 AND wtaxonomy.count > 0");
$catCounter = 0;
foreach ($catQuery as $category) {
$catCounter++;
$catStyle="";
if (is_int($catCounter / 2)) $catStyle=" class="catAlt"";
$catLink = get_category_link($category->term_id);
echo '<li'.$catStyle.'><h3><a href="'.$catLink.'" title="'.$category->name.'">'.$category->name.'</a></h3>';
echo '<ul style="margin-left:15px;">';
query_posts('category__in='.$category->term_id.'&showposts=5');?>
<?php while (have_posts()) : the_post(); ?>
<li><a href="<?php the_permalink() ?>" rel="bookmark" title="<?php the_title(); ?>"><?php the_title(); ?></a></li>
<?php endwhile; ?>
<li><a href="<?php echo $catLink; ?>" title="<?php echo $category->name; ?>">More <strong><?php echo $category->name; ?></strong></a></li>
<li> <?php
$sub_cat_id = $category->term_id;
$get_sub_args = array('child_of' =>$sub_cat_id);
$categories_arr = get_categories($get_sub_args);
//print_r ($categories_arr);
foreach ($categories_arr as $sacategory) {
//Display the sub category information using $category values like $category->cat_name
echo '<h2>'.$sacategory->name.'</h2>';
echo '<ul style="margin-left:15px;">';
foreach (get_posts('cat=".$sacategory->term_id) as $post) {
setup_postdata( $post );
echo "<li><a href="'.get_permalink($post->ID).'">'.get_the_title().'</a></li>';
}
echo '</ul>';
}
?></li>
</ul>
</li>
<?php } ?>
</ul>
<!-- Category Archive End -->
</div>