Get theme mods that fall back to the stored parent theme mod if child theme is active.

parent-theme-mod-fallback.php

<?php
/**
 * The purpose of this code is to show how you can use theme mods that will fall back to
 * the already-set mods of the parent theme.  So, when a child theme is active, the code 
 * checks, in the following order:  1) child theme mod, 2) parent theme mod, 3) default.
 */

function jt_get_theme_mod( $name, $default = false ) {

	if ( is_child_theme() )
		return get_theme_mod( $name, jt_get_parent_theme_mod( $name, $default ) );

	return get_theme_mod( $name, $default );
}

function jt_get_parent_theme_mods() {

	$slug = get_option( 'template' );

	return get_option( "theme_mods_{$slug}", array() );
}

function jt_get_parent_theme_mod( $name, $default = false ) {
	$mods = jt_get_parent_theme_mods();

	if ( isset( $mods[ $name ] ) )
		return $mods[ $name ];

	if ( is_string( $default ) )
		$default = sprintf( $default, get_template_directory_uri(), get_stylesheet_directory_uri() );

	return $default;
}