Getting categories and posts with custom output

Right now I have this:

<?php
    $category = get_category_by_slug( 'collections' );
    wp_list_categories('child_of='.$category->term_id);
?>

I want to be able to customize the output but also list the children posts of these categories like this and I also want to customize the layout (each sub category has an image attached to it):

Parent Category
Sub Cat 1
Post 1
Post 2
Sub Cat 2
Post 1
Post 2