If I'm not mistaken, it is normal that you do not have the layout after $view_helper->action('exemple', 'Mycontroller','mymodule');
Indeed, the layout is call in postDisatch() of Zend_Layout_Controller_Plugin_Layout
's plugin.
You can still try this:
In your layout 'mail.phtml' put this:
echo $this->layout()->content;
In your method :
$view_helper = new Zend_View_Helper_Action();
$html_content = $view_helper->action('exemple', 'Mycontroller','mymodule');
$layout_path = $this->_helper->layout()->getLayoutPath();
$layout_mail = new Zend_Layout();
$layout_mail->setLayoutPath($layout_path) // assuming your layouts are in the same directory, otherwise change the path
->setLayout('mail');
// Filling layout
$layout_mail->content = $html_content;
// Recovery rendering your layout
$mail_content = $layout_mail->render();
var_dump($mail_content);