How to receive meeting invitations from Office365, so that they can be parsed and added to a calendar

How to receive iCalendar (.ics or .ical) meeting invitations from
outlook.office365.com, so that they can be parsed and added to a
calendar (such as remind + wyrd)?

I've searched long and hard for an answer, but haven't found any, so I
wonder if I'm just missing something really trivial.

I am using Mutt 1.5.22 with OfflineIMAP 6.5.5 on Fedora 20 (Heisenbug).

There are many scripts out there for parsing iCalendar messages into
formats that can be imported into calendars. This is not my problem.
My problem is that I'm not even receiving iCalendar messages, so I have
nothing to parse.

A meeting invitation arrives in my inbox as a base64 encoded text/html
message. It is not a multipart message and there are no attachments.
The body of the message contains a link to Microsoft Outlook Web
Access (OWA). Following the link doesn't seem to do anything except
take me to WebMail. The rest of the email body contains the description
of the meeting invitation.

I tried forwarding the invite and forwarding the invite as an
attachment, but neither of these affected the format of the message.

I inspected the headers of the message, but nothing stood out as being
important. I've copied them here, in case they mean something to
anyone:

Received: from [...] by [...] with Microsoft SMTP Server (TLS) id
        [...] via Mailbox Transport; [timestamp]
Received: from [...] by [...] with Microsoft SMTP Server (TLS) id
        [...]; [timestamp]
Received: from [...] by [...] with Microsoft SMTP Server (TLS) id
        [...]; [timestamp]
Received: from [...] by [...] with mapi id [...]; [timestamp]
From: [meeting organiser]
To: [meeting attendees]
Subject: [meeting subject]
Thread-Topic: [meeting subject]
Thread-Index: [...]
Sender: [sender on behalf of meeting organiser]
Date: [timestamp]
Message-ID: <[...]>
Accept-Language: en-US
Content-Language: en-US
X-MS-Exchange-Organization-AuthAs: Internal
X-MS-Exchange-Organization-AuthMechanism: 03
X-MS-Exchange-Organization-AuthSource: [...]
X-MS-Has-Attach:
X-MS-Exchange-Organization-SCL: -1
X-MS-TNEF-Correlator:
Content-Type: text/html; charset="utf-8"
Content-Transfer-Encoding: base64
MIME-Version: 1.0

I also inspected the headers of the message in WebMail. There were
more headers (some related to tnef), but again, nothing seemed related
to calendars or invitations.

I compared the headers of a "meeting invite" with the headers of a
normal email. The only difference was that a normal email contains an
extra header: "X-Auto-Response-Suppress: DR, RN, NRN, OOF, AutoReply".

My .offlineimaprc's folderfilter is set to not sync the Calendar folder.
This is because every time OfflineIMAP tried to sync, it would run into
over a hundred instances of the same error when syncing the Calendar
folder: "ERROR: IMAP server 'remote' does not have a message with
UID '[…]'."

Using Python's imaplib to inspect the Calendar folder:

>>> import imaplib
>>> i = imaplib.IMAP4_SSL("outlook.office365.com", 993)
>>> i.login("NAME@COMPANY.com", "PASSWORD")
('OK', ['LOGIN completed.'])
>>> i.select("Calendar")
('OK', ['159'])
>>> i.fetch(159, "(RFC822)")
('OK', [None])
>>> i.fetch(159, "(RFC822)")

The second time I call fetch, it returns a message: "The server couldn't
retrieve the following message. The message hasn't been deleted. You
might be able to view it using either Outlook or Outlook Web App. You
can also contact the sender to find out what the message says."

In WebMail, I see that the Calendar folder (accessible via the
Calendar tab) has permissions for visibility outside organization.
It's currently set to "Not shared". Other options are "Availability
only", "Limited details", or "Full details". Setting the permissions
to "Full details" and then sending a meeting invitation to myself
didn't have any effect on the format of the meeting invite.

As a workaround for not receiving iCalendar message, I have Thunderbird
open with the Lightning add-on. Somehow, the Lightning add-on knows how
to receive meeting invitations. The messages still show up as
text/html, but there's a link in Thunderbird's status bar. Clicking it opens a
prompt asking whether to deny or accept the invitation.

Anyone have any ideas why meeting invitations from Outlook 365 are
arriving as simple text/html messages rather than iCalendar messages?
Is there anything I can do? If the Lightning add-on can work with the invitations, then there must be a solution, such as using Microsoft Exchange Web Services (EWS). If the solution will require me to code up a tool, so be it. A push in the right direction would be greatly appreciated.