/**
 * Create HTML list of nav menu items and allow HTML tags.
 * Replacement for the native menu Walker, echoing the description.
 * This is the ONLY known way to display the Description field.
 *
 * @see http://wordpress.stackexchange.com/questions/51609/
 *
*/
class Description_Walker extends Walker_Nav_Menu {

    function start_el(&$output, $item, $depth, $args)
    {
        $classes     = empty ( $item->classes ) ? array () : (array) $item->classes;

        $class_names = join(
            ' '
        ,   apply_filters(
                'nav_menu_css_class'
            ,   array_filter( $classes ), $item
            )
        );

        ! empty ( $class_names )
            and $class_names = ' class="'. esc_attr( $class_names ) . '"';

        // Build default menu items
        $output .= "<li id='menu-item-$item->ID' $class_names>";

        $attributes  = '';

        ! empty( $item->attr_title )
            and $attributes .= ' title="'  . esc_attr( $item->attr_title ) .'"';
        ! empty( $item->target )
            and $attributes .= ' target="' . esc_attr( $item->target     ) .'"';
        ! empty( $item->xfn )
            and $attributes .= ' rel="'    . esc_attr( $item->xfn        ) .'"';
        ! empty( $item->url )
            and $attributes .= ' href="'   . esc_attr( $item->url        ) .'"';

        // Build the description (you may need to change the depth to 0, 1, or 2)
        $description = ( ! empty ( $item->description ) and 1 == $depth )
            ? '<span class="nav_desc">'.  $item->description . '</span>' : '';

        $title = apply_filters( 'the_title', $item->title, $item->ID );

        $item_output = $args->before
            . "<a $attributes>"
            . $args->link_before
            . $title
            . '</a> '
            . $args->link_after
            . $description
            . $args->after;

        // Since $output is called by reference we don't need to return anything.
        $output .= apply_filters(
            'walker_nav_menu_start_el'
        ,   $item_output
        ,   $item
        ,   $depth
        ,   $args
        );
    }
}

// Allow HTML descriptions in WordPress Menu
remove_filter( 'nav_menu_description', 'strip_tags' );
add_filter( 'wp_setup_nav_menu_item', 'cus_wp_setup_nav_menu_item' );
function cus_wp_setup_nav_menu_item( $menu_item ) {
     $menu_item->description = apply_filters( 'nav_menu_description', $menu_item->post_content );
     return $menu_item;
}

and then use this in your template:

<?php wp_nav_menu( array( 'walker' => new Description_Walker )); ?>