From http://www.oracle.com/technetwork/java/faq-135477.html#sendmpa:
You'll want to send a MIME multipart/alternative message. You construct such a message essentially the same way you construct a multipart/mixed message, using a MimeMultipart object constructed using new MimeMultipart("alternative"). You then insert the text/plain body part as the first part in the multpart and insert the text/html body part as the second part in the multipart. You'll need to construct the plain and html parts yourself to have appropriate content. See RFC2046 for details of the structure of such a message.
Can someone show me some sample code for this?