ActionMailer multipart: html, plain and attachment?

Has anyone gotten emails to work where you specify the HTML and the
plain text alternatives, but also include an attachment?

Reason I'm asking: I'm sending out event notices, styled as HTML but
with a plain text alternative. I also want to attach the .ics file.

For some reason, I can't get this to work. If I explicitly put in
"multipart/mixed" (to support the attachment) it won't do the two
alternatives. If I explicitly put in "multipart/alternative" (to
support the HTML and plain text parts), it won't show the attachment.

Is this a Rails/ActionMailer issue or am I just missing something with
how these multipart messages are supposed to be put together?