I've got some progress, but not yet completely there.
When using MailMessage class and LoadContent instead of MimeMessage I actually got the message through. It comes with correct HTML body, but the images appear as attachments in MS Outlook and the email window fails to display/find them. They are displayed as red crosses.
How's your problem. I have checked the MailMessage.Load and MailMessage.LoadContent. All of them can produce proper output. The email can show images without problem.
Please check the attachment -- the snapshot. Let me know if you need any help.
Among few other things it did not like mime part urls such as file://image.001.png. In this case the images appeared as attachments in Outlook, not as images in the message. I changed them to “image.001.png” and that worked better.