Try this: put the form php code in a php file (different from newslettersubscription.php, which you also need) and upload it to your server (form.lib.php has to be there too). Then create a new plugin using hook location global_start and this code:
PHP Code:
ob_start();
include('formcode.php');
$mailform = ob_get_contents();
ob_end_clean();
vB_Template:preRegister('newsletter_subscription', array('mailform' => $mailform));
(You can change 'formcode.php' to be whatever you named the file).
Then in your newsletter_subscription template, put {vb:raw mailform} where you want the form.