How to send out HTML email with mailgun?

Question 1

I have used external html template in this way. It may be help you.

$html  = file_get_contents('my_template.html'); // this will retrieve the html document

and then:

$result = $mgClient->sendMessage("$domain",
       array('from'    => 'My Business Name <me@samples.mailgun.org>',
             'to'      => 'name-1@gmail.com, name-3@gmail.com, name-3@gmail.com',
             'subject' => 'Issue Feb 2014',
             'text'    => 'Your mail do not support HTML',
             'html'    => $html,
             'recipient-variables' => '{"name-1@gmail.com": {"first":"Name-1", "id":1}, "name-2@gmail.com": {"first":"Name-2", "id": 2}}'), 
       array('inline' => 'Pad-Thai-1.jpg'));

Check this line:

'html'    => $html,

Question 2

Adding a link to Mailgun documentation. This helped me while constructing HTML and MIME messages. https://documentation.mailgun.com/api-sending.html#examples

As per documentation:

# Include the Autoloader (see "Libraries" for install instructions)
require 'vendor/autoload.php';
use Mailgun\Mailgun;

# Instantiate the client.
$mgClient = new Mailgun('YOUR_API_KEY');
$domain = "YOUR_DOMAIN_NAME";

# Make the call to the client.
$result = $mgClient->sendMessage($domain, array(
    'from'    => 'Excited User <YOU@YOUR_DOMAIN_NAME>',
    'to'      => 'foo@example.com',
    'cc'      => 'baz@example.com',
    'bcc'     => 'bar@example.com',
    'subject' => 'Hello',
    'text'    => 'Testing some Mailgun awesomness!',
    'html'    => '<html>HTML version of the body</html>'
), array(
    'attachment' => array('/path/to/file.txt', '/path/to/file.txt')
));