The world must serve the story, not the other way around.
I think you have an advantage over, let's say Tempest, by having your story occur on an altered version of the real world. I might be wrong, but as far as I can see, the world in Anathema is pretty much the same as our world up until 2010. That will help you greatly because you won't have to hold the hand of your readers when it comes to the way the world itself works, its history and culture; its nations and their politics; the level of technology, etc.
The other advantage you have over other works of fiction is that, speaking in general terms, Chris and Sarina are both relatively new to that part of your world that is different from ours. Why is it an advantage? Because they can draw attention to the fantastic elements of your world and not look foolish while doing it.
Familiarity breeds apathy. If you saw someone driving a car down the street, what would you think? What do you think about someone using a smartphone to take a picture of themselves? What is your opinion on indoor plumbing? I don't know about you, but for me, the response would be something along the lines of "meh". Ask the same thing to someone who has never seen those things, and the response will be vastly different.
You could exploit that very same principle. Do your characters know enough about their world to be apathetic towards the fantastic elements? Do they even care? If they care, is just mild curiosity or their interest is bordering in obsession?
The answer you give will show you the way to dealing with exposition in dialogue. For example, if one of your characters doesn't care about the things that happen around the world, would they know who Shanti is? Would they know what is the Covenant? Would they know the UN is involved? Would they even know the people with superpowers are actually wearing costumes and doing heroic/dastardly deeds? If the answer is 'no', you could have a good and easy way to deliver a bit of information.
"Shanti is only the greatest hero this world has ever known. I can't believe you don't know that, dude. Do you live under a rock or something?
That's another thing, it is better to deliver exposition through action and dialogue than through description alone. And don't think the third-person limited POV makes it harder to deliver the exposition; internal monologues aren't that good. I mean, unless you're a Hollywood Schizophrenic, who is going to listen to your beautiful explanation on the laws and customs of costumed heroes?
Although, tropes are not bad and you can make that work. What if one of your characters likes talks to himself/herself? Maybe he or she needs to make an important decision so they find a mirror and start talking to themselves, delivering another bit of exposition along the way.
"Should I join the Covenant? If I do I'd have to fight the bad guys under the banner of the United Nations. What do you think?" She let out a sigh when the cat gave her a confused look. "I know you can't really talk. Pretending you can helps me think, okay? Please don't judge me."
Finally, there's the approach of treating the fantastic elements of your world like something relatively normal. What this means is that you don't necessarily have to explain every little detail of your world. Mentioning a random quirk of your world doesn't mean you have to explain it right away. If you infer the nature of the thing that is being mentioned (Is it good or bad? Is it safe or harmful? Can it be eaten?), then you can deliver the explanation bit by bit over a long period of time.
For example, in A Song of Ice and Fire, we're introduced to the Others and Wights in the very first chapter (prologue), but at that point we still don't understand what they really are, how they work, what they want, etc. All we know is that they are bad news for anyone unlucky enough to find one. Also, we know that they're not exactly what you'd call 'normal' in our world. So there.
TL;DR: Use dialogue and action to deliver exposition but remember you don't have to explain everything right away and, in some cases, at all.