Let's take an example:
You're studying for a test and your classmate/roommate comes in and says:
The teacher posted a study guide for us... and, he's pushed the test back a day, so we have more time to study.
Those are two separate things but they are related because they have to do with the test. Still, it was told to you in one event, so you can consider it to be a single "piece of news", so "That's great news!" is still a perfectly appropriate response.
If you really want to emphasize that it's two different things, you might consider using "some" or "both".
That's some great news.
Both of those pieces of news are great to hear.
The latter of these options seems a little odd but I can imagine saying it if I really wanted to emphasize that both are great to know. For example, you might continue the sentence:
Both of those pieces of news are great to hear since I wasn't sure what to study for the test and I really don't think I'm prepared to take it tomorrow.
You could also not use "news" at all.
I'm so glad to hear that.
That's great to hear.
Even if the two pieces of news aren't related, it's fine to combine them:
I got an A on my astronomy test... Also, Jane is coming to visit in a week!
Replying "That's great news" is still perfectly acceptable. Remember, you're likely to respond individually to both pieces of news in a following sentence:
That's great news! I know you studied really hard for your test... and I'm so excited to see Jane. I haven't seen her in three months.