I don't think this is possible, based on your requirements.
A screen-reader user, or any user for that matter, would have to decipher what is a news item and what is an event item.
If you can't organize them by separate lists, then maybe change the link text to make it understandable.
Ex. "News | News Item 1" or "Event | Event Item 1"
good question btw ;)
Grabbing your example:
<h2>Our latest News and Events</h2>
<li>news item 1</li>
<li>news item 2</li>
<li>news item 3</li>
<li>event item 1</li>
<li>event item 2</li>
I used to do something more like this with ...