CDOSYS And Multipart

I have a form that triggers the sending of an e-mail via CDOSYS. I'd
like to make this a nice HTML-formatted multipart message, but for some
reason the text version is coming through blank.

Originally I thought I had read that CDO has an automatic text converter
that will turn the HTML code into a plain TEXT message, but when that
didn't work (and I couldn't find anything further about it), I added a
custom text line like this:

objMessage.TextBody = "This is the text body."
objMessage.HTMLBody = "This is where I put the long HTML code."
objMessage.send

That worked in my mail client (Thunderbird), but the messages still go
blank in my wife's Hotmail account (actually, if I send it directly to
her hotmail account they don't arrive at all; if I send it to her other
address that forwards to her hotmail account, they come in, but the body
is blank).