GMail displays plain text email instead HTML

Try switching the order of the parts of the message, putting the HTML part after the plain-text part. It might work :).

NOTE: I cannot remember now where I read this (or if I for sure even did), but the reason switching might help is because I think the preferred part of the message may be the last part.

Update: I found a place where it says that parts in a multipart MIME message should be in order of increasing preference -- here, in section 7.2.3 (edit: latest version here; thanks @ALEXintlsos!), starting with the third to last paragraph.

Update: Here is a quote of section 7.2.3, (see https://stackoverflow.com/help/referencing):

7.2.3 The Multipart/alternative subtype
The multipart/alternative type is syntactically identical to multipart/mixed, 
but the semantics are different. In particular, each of the parts is an
"alternative" version of the same information. User agents should recognize
that the content of the various parts are interchangeable. The user agent
should either choose the "best" type based on the user's environment and
preferences, or offer the user the available alternatives. In general, choosing
the best type means displaying only the LAST part that can be displayed. This
may be used, for example, to send mail in a fancy text format in such a way
that it can easily be displayed anywhere:

From:  Nathaniel Borenstein <[email protected]> 
To: Ned Freed <[email protected]> 
Subject: Formatted text mail 
MIME-Version: 1.0 
Content-Type: multipart/alternative; boundary=boundary42 


--boundary42 
Content-Type: text/plain; charset=us-ascii 

...plain text version of message goes here.... 

--boundary42 
Content-Type: text/richtext 

.... richtext version of same message goes here ... 
--boundary42 
Content-Type: text/x-whatever 

.... fanciest formatted version of same  message  goes  here 
... 
--boundary42-- 

In this example, users whose mail system understood the "text/x-whatever"
format would see only the fancy version, while other users would see only the
richtext or plain text version, depending on the capabilities of their system.

In general, user agents that compose multipart/alternative entities should
place the body parts in increasing order of preference, that is, with the
preferred format last. For fancy text, the sending user agent should put the
plainest format first and the richest format last. Receiving user agents should
pick and display the last format they are capable of displaying. In the case
where one of the alternatives is itself of type "multipart" and contains
unrecognized sub-parts, the user agent may choose either to show that 
alternative, an earlier alternative, or both.

NOTE: From an implementor's perspective, it might seem more sensible to reverse
this ordering, and have the plainest alternative last. However, placing the
plainest alternative first is the friendliest possible option when
multipart/alternative entities are viewed using a non-MIME- compliant mail
reader. While this approach does impose some burden on compliant mail readers,
interoperability with older mail readers was deemed to be more important in
this case.

It may be the case that some user agents, if they can recognize more than one
of the formats, will prefer to offer the user the choice of which format to
view. This makes sense, for example, if mail includes both a nicely-formatted
image version and an easily-edited text version. What is most critical, however,
is that the user not automatically be shown multiple versions of the same data.
Either the user should be shown the last recognized version or should 
explicitly be given the choice.