Message template with mail key
Templates must be put in the theme's directory, not in the Mime Mail module directory or in your own custom module directory. The Mime Mail documentation explains the proper template naming and location. See https://www.drupal.org/docs/7/modules/mime-mail/theming-html-mail-sent-through-mime-mail
The most specific template name should have three parts, separated by &quot;--&quot;. These parts are:

&quot;mimemail-message&quot; This is the same for all templates.
&quot;modulename&quot; This is the machine name of the module that provides the hook_mail() implementation used to send the mail. This is also the module name that appears as the first argument to your drupal_mail() call.
&quot;key&quot; This is an identifier used to differentiate multiple emails sent by the same module. This appears as the second argument to your drupal_mail() call.

Any underscores appearing in the &quot;modulename&quot; or the &quot;key&quot; should be replaced by dashes.
For example, if my module has a machine name of &quot;example_module&quot; and the mail key is &quot;example_key&quot; then the specific template name, used just for email with that key sent by that module, should be:
  mimemail-message--example-module--example-key.tpl.php

The documentation for drupal_mail() explains a number of these things. See https://api.drupal.org/api/drupal/includes%21mail.inc/function/drupal_mail/7.x