What is the correct way to send multipart email in wordpress?

Do you mean to send a plain text version along-side the HTML version?

If so I found this page helpful in setting it up:

The crux of it comes down to this:

 //create a boundary for the email. This 
 $boundary = uniqid('np');

 //headers - specify your from email address and name here
 //and specify the boundary for the email
 $headers = "MIME-Version: 1.0\r\n";
 $headers .= "From: Your Name \r\n";
 $headers .= "To: ".$email."\r\n";
 $headers .= "Content-Type: multipart/alternative;boundary=" . $boundary . "\r\n";

 //Plain text body
 $message .= "Hello,\nThis is a text email, the text/plain version.
 \n\nRegards,\nYour Name";
 $message .= "\r\n\r\n--" . $boundary . "\r\n";
 $message .= "Content-type: text/html;charset=utf-8\r\n\r\n";

 //Html body
 $message .= "
  Hello,
 This is the html version.

 Regards,
 Your Name";
 $message .= "\r\n\r\n--" . $boundary . "--";

Hope this helps