How to display author post count for multiple custom post types?

This ticket was fixed and closed in version 4.3.

Make sure you got the latest version ( currently 4.4.2 )

If we check out the inline documentation for the count_user_posts() we find this part:

* @since 4.3.0 Added `$public_only` argument. Added the ability to pass an array
*              of post types to `$post_type`.

Note the default post type for that function is post.

So you will most likely have to add the post types you want, here’s an example:

echo count_user_posts( 
    $userid = 1, 
    $post_type = [ 'post', 'page' ], 
    $public_only = false 
);

to get the count for the user with user id as 1 and post types post and page.