Getting custom HTML to show in homepage.php - wordpress

Question

I have to add some simple HTML to the homepage of a client's WordPress website. At first, I added the code to the header.php and everything looked and worked how it should; but, then I realised that it was showing on every page when I just need it on the home page.
So, I tried adding the same HTML after the get_header in the homepage.php and then in the index.php but nothing shows at all when I add the code to these pages.
No matter where I put the HTML in homepage.php or index.php it will not show. I'm new to WordPress as you have no doubt gathered.
Do I need to make a template or use some code to introduce the HTML in either of these two pages? Why does it show in the header.php?
I tried using with no joy:
if ( is_home() ) {
The home page code is here if it helps:
<?php
/**
Template Name: Homepage
*
*/
get_header(); ?>
<?php $general_options = get_option( 'meanthemes_theme_general_options' ); ?>
<?php $content_options = get_option ( 'meanthemes_theme_content_options' ); ?>
<?php if( isset( $general_options[ 'hide_slider' ] ) ) {
// do nothing
} else {
?>
<section class="hero flexslider">
<article class="wrapper">
<div class="flex-container"></div>
<ul class="slides">
<?php
$bannerPortfolio = $general_options[ 'swap_slider' ];
if(!$bannerPortfolio) {
query_posts( array ( 'posts_per_page' => 3 ) );
while ( have_posts() ) : the_post();
?>
<li>
<h2>
<?php the_title(); ?>
</h2>
<div>
<?php echo excerpt_clip(get_the_excerpt(), '28'); ?> <?php _e('[...]','meanthemes'); ?>
</div>
<time class="time" datetime="<?php the_time('Y-m-d', '', ''); ?>"><?php the_time('jS M Y') ?></time>
</li>
<?php endwhile; wp_reset_query(); ?>
<?php
} else {
?>
<?php
query_posts( array( 'post_type' => 'portfolio', 'order' => 'desc', 'posts_per_page' => '3' ) );
?>
<?php if ( have_posts() ) while ( have_posts() ) : the_post(); ?>
<li>
<hgroup>
<h2>
<?php the_title(); ?>
</h2>
<div>
<?php echo excerpt_clip(get_the_excerpt(), '48'); ?> <?php _e('[...]','meanthemes'); ?></div>
</hgroup>
</li>
<?php endwhile; ?>
<?php } ?>
</ul>
</article><!-- / article.wrapper -->
</section>
<script>
jQuery(window).load(function() {
jQuery('.flexslider').flexslider({
animation: "fade", // animation type fade or slide
slideshowSpeed: <?php echo sanitize_text_field( $general_options ['slider_timer'] ); ?>, // sections between transitions
directionNav: true, // show previous and back
controlNav: false,
controlsContainer: '.flex-container'
});
});
</script>
<?php } ?>
<?php if( $general_options[ 'show_portfolio' ] ) { ?>
<section class="wrapper portfolio">
<article>
<hgroup>
<h2><?php echo balanceTags( $content_options['we_do'] ); ?></h2>
</hgroup>
<div><?php echo balanceTags( $content_options['we_do_summary'] ); ?></div>
</article>
<?php
query_posts( array( 'post_type' => 'portfolio', 'posts_per_page' => '4', 'orderby' => 'date', 'order' => 'desc' ) );
?>
<?php if ( have_posts() ) while ( have_posts() ) : the_post(); ?>
<aside>
<?php the_post_thumbnail('portfolio-thumb'); ?>
<hgroup>
<h3><?php the_title(); ?></h3>
</hgroup>
<div><?php echo excerpt_clip(get_the_excerpt(), '14'); ?><?php _e('[...]','meanthemes'); ?></div>
</aside>
<?php endwhile; wp_reset_query(); ?>
</section>
<?php } ?>
<script>
jQuery(document).ready(function() {
jQuery('body').addClass("home");
});
</script>
<?php get_footer(); ?>

Answer 1

Howlin's example should work. Another solution is to create a front-page.php in the theme-directory, copy the content from the page.php to it, and add your specific HTML-Code for the homepage (frontpage).
Visit http://codex.wordpress.org/Template_Hierarchy to understand which template is invoked in which case.
Visit http://codex.wordpress.org/Conditional_Tags for Conditional Tags, which you can use e.g. in theheader.php

Answer 2

You might need to try is_front_page instead.
if(is_front_page()){
is_home works if you have blog posts displaying on the homepage and is_front_page if the homepage is set as a static page.