The source of this problem isn’t your form or Dreamhost, it is the formmail.cgi file that you’re trying to use. It supports any number of input fields, but not file uploads. You don’t get anything with the correct enctype, because it is ignoring uploaded files as designed. When you use the invalid enctype, the file field is coming through as a simple text input, which is why you’re getting the actual string in that field. Formmail details here: http://formmail.dreamhost.com/
You may be able to find a premade PHP handler page on the net, but you’ll need to write your own if not. You have a couple options that might prove useful. You could build a custom handler page that is tailored to your form, constructs an email from it, and includes the uploaded files as attachments.