It sounds like you want to hook into pre_get_posts for the blog index. The following should only effect the blog index. That is what is_home() is for. Of course, you can edit the function to alter that behavior if you want.
function add_post_type_to_index_wpse_88317($qry) {
if (is_home()) {
$qry->set('post_type',array('post','movies_cp')); // plus any others you want.
}
}
add_action('pre_get_posts','add_post_type_to_index_wpse_88317');
That post type is from another question on this site somewhere. I used it because I could test it on my server. You will need to make that match the name you used to register your post type.