It looks like you need to add your news custom post type to the query for archive pages (I had the same problem).
Codex: custom post types to query
Add this code to your functions
// Show posts of 'post', and 'news' post types on archive page
add_action( 'pre_get_posts', 'add_my_post_types_to_query' );
function add_my_post_types_to_query( $query ) {
if ( is_archive() && $query->is_main_query() )
$query->set( 'post_type', array( 'post', 'news' ) );
return $query;
}
Just check that your admin post listings are not affected.