Had this strange problem at a customers Exchange 2013 environment that emails, which are composed as HTML Mails are being received as text-only messages.
After looking at some more obvious things i started the exchange powershell and executed the following command:
get-remotedomain | fl
Here i spotted that the content type was set to MimeText. That value needs to be changed to MimeHtmlText with:
get-remotedomain | set-remotedomain -ContentType MimeHtmlText
A nice side effect of this, all of our wrong character set problems were suddenly gone too. German umlauts are now appearing properly for the recipient instead a wild mixture of ???.