I had the same problem, what I do is something like:
// Add filter for registration email body
add_filter('wp_mail','handle_wp_mail');
function handle_wp_mail($atts) {
/*"Your username and password" is the subject of the Email WordPress send from "function wp_new_user_notification" in file "wp-includes/pluggable.php"*/
if (isset ($atts ['subject']) && substr_count($atts ['subject'],'Your username and password')>0 ) {
if (isset($atts['message'])) {
$atts['message'] = 'new body';
}
}
return ($atts);
}