What kind of permission module are you using ? Is it possible you implement yourself these permission ?  

I would restrict node access to anonymous user using a custom module implementing [`hook_node_access()`][1] and allow them to see the nodes on the front page (using the function [`drupal_is_front_page()`][2]):

<!-- language: lang-php -->

    function MYMODULE_node_access($node, $op, $account) {
      if ($op == 'view' && $account->uid == 0) {
        if (drupal_is_front_page()) {
          return NODE_ACCESS_ALLOW;
        } else {
          return NODE_ACCESS_DENY;
        }
      }
      return NODE_ACCESS_IGNORE;
    }


  [1]: http://api.drupal.org/api/drupal/modules--node--node.api.php/function/hook_node_access/7
  [2]: http://api.drupal.org/api/drupal/includes--path.inc/function/drupal_is_front_page/7