Custom post(page) type, template dropdown gone.

Hello.
Similar problems has been posted before, but most times it’s been about a custom post type. I haven’t find any solution, googling very much for a solution where I got nowhere. So now I’m looking for your help to find a solution to my problem.

The problem:
I have my custom post type (acting like a page) where the template dropdown in the admin is not visible. I have a custom template file with this comment on top, and I have made custom template files before:

/*
Template Name: family-page
*/

And I am using these arguments + function to create the custom post type:

add_action( 'init', 'create_post_type' );
function create_post_type() {
	register_post_type('familjer', array(
		'label' => __('Familjer'),
		'singular_label' => __('Familjer'),
		'public' => true,
		'show_ui' => true, // UI in admin panel
		'_builtin' => false, // It's a custom post type, not built in!
		'_edit_link' => 'post.php?post=%d',
		'capability_type' => 'page',
		'menu_order' => true,
		'hierarchical' => true,
		'rewrite' => array("slug" => "%author%"), // Permalinks format
		'supports' => array('title', 'excerpt', 'editor', 'thumbnail', 'page-attributes'),
		'menu_position' => 4
	));
}

Any clue on what could be wrong? I do see the order and the parent dropdown in the page-attributes sidebar, but not the template dropdown. It works as expected on the regular “Pages” menu, but not in my custom menu, in this case “Familjer”.

Thanks in advance.