This is a duplicate of the question at the following address, because the answer provided there is incorrect, and I don't have the reputation points to comment or otherwise correct it:
The answer provided by dordio does not actually answer the question.
I want to give credit to user "BMANN2" on Reddit, from this thread:
https://m.reddit.com/r/apple/comments/3lameq/ios_9_calendar_widget_not_showing_whole_day/
Since I can only post two URLs with my rep, here's a very shortened, simplified version of his response without his links to images:
1) Open calendar app.
2) Once in Calendar, switch to a different viewing mode, then pull down the NC. It should switch the Today widget view to match what you see in Calendar.
For his full answer, look for the post that starts with "Ok I seem to have found out how to do it, it is somewhat like what was mentioned by Vanitas1440."
This seems to only work if you switch viewing modes then pull down the NC without switching to another app entirely in between. If you come back to Calendar from another app, then pull down the NC, the change doesn't take effect.
The first time I tried this method, it didn't work, because I went to the calendar app, and the view I wanted (list view) was already onscreen, so I pulled down the NC, and nothing happened.
However, I then switched the view in calendar to the layered day view, then pulled down NC and "Today" updated to the new view.... so any view can be used.
Once I changed the view back to the one I actually wanted and pulled down the NC again, now my Today view widget is set to the proper one.
I hope this helps!
If anyone wants to merge this into the other thread, feel free.
