Hi — I’ve searched the support to find an answer to exactly the same question, but didn’t find it.
Browsing through the WP-code, I finally found a function called get_post_type(), which allowed me to do the trick! You can retrieve the post-type for a certain post/page, by use get_post_type($id) in the loop.
<?php if (have_posts()) : ?>
while (have_posts()) : the_post();
$posttype = get_post_type($id);
if ($posttype == 'post') { ?>
Content on how you want to show POSTS.
<?php } else { ?>
Content on how you want to show PAGES.
<?php } ?>