It’s pretty easy to inject content between posts if you have direct access to The Loop in the theme:

$counter = 0;

while ( have_posts() ) : the_post();
	
	if ( 1 == $counter )
		echo '<div>Some banner</div>';

	$counter++;

	// the_title() etc.

endwhile;

If you want to do this without modifying the theme, the solution is not so obvious, but it exists:

function insert_between_posts( $post ) {
	global $wp_query;

	// Check if we're in the main loop
	if ( $wp_query->post != $post )
		return;

	// Check if we're at the right position
	if ( 1 != $wp_query->current_post )
		return;

	// Display the banner
	echo '<div>Some banner</div>';
}
add_action( 'the_post', 'insert_between_posts' );

Note that with this second approach, the banner will be displayed throughout the site. Fortunately, this can be easily controlled using conditional tags:

function insert_between_posts( $post ) {
	global $wp_query;

	// Check if we're in the right template
	if ( ! is_home() )
		return;

	// Check if we're in the main loop
	if ( $wp_query->post != $post )
		return;

	// Check if we're at the right position
	if ( 1 != $wp_query->current_post )
		return;

	// Display the banner
	echo '<div>Some banner</div>';
}
add_action( 'the_post', 'insert_between_posts' );

I hope this gives you some ideas for your next great plugin or child theme. Happy hacking!