a bit old-school and the humans aren't aware there are vampires in their midst but Vampire Idol is an old and hilarious fave - it's a sitcom from 2011 that happened to mark the acting debut of a certain Mr Kim Woo-bin as one of the titular vampires, who shack up in a dorm run by a female idol agency.

The covering-up here is being done by the vampires to hide it from their humans, but it's adorable and hilarious (and hopefully fully subbed by now?!)

My Girlfriend Is A Gumiho

Do shows like Rooftop Prince and Kill Me Heal Me count?

There are soooo many in Goblin.
One of the big ones is when Eun tak is able to move the sword from Goblins chest for the first time. Goblin is surprised but also in a huge amount of pain and pushes her hand away from the sword sending her flying in the air. She is about to crash into the side of a truck and Goblin comes to the rescue to save her but in doing so wipes out the whole car park where the truck is parked. Reaper is sent to erase the memory of the general public who witnessed the event and Deok hwa provides monetary payment for the damaged cars. Meanwhile a team of company workers are tasked to erase any footage of the event found online.

ARE YOU HUMAN TOO comes to mind. The robromance Nam Shin III had with Young Hoon was sweet! I think the scene after the club fire was the first time Young Hoon had to cover for Shin, quite literally too. Of course the whole bit where they trained robo Nam Shin in simulation to help him assume the human Nam Shin was delighful!

This isn't EXACTLY what OP is asking, but My Holo Love has a lot of great hijinks where the human ML has to pretend to be the hologram 2ML, and IIRC the other characters have to help out with that.

There are some humans but from the past who needed some cover like in Rooftop Prince.

Otherwise, the mermaid in Legend of the Blue Sea.

I didn't watch The Bride of Habaek, but I think at least there was the cohabitation theme.

I'm pretty sure there's lots in BEAUTY INSIDE. I remember the ML covering the FL with his jacket a couple to times to save her from getting recognized (or not recognized because she's transformed?). Also a lengthy segment where the FL looks like a highschool boy and ML accepted suspicions that he likes minors/boys, and that he had a son at a young age.

It doesn’t parallel the work our FL is doing in HeartBeat directly, but the example drama that I have seen and think fits best, is Delivery Man. In this drama our ML can see ghosts, and the plot revolves around him fronting for these paranormal creatures, all of whom have things they need to do in this world, but who can’t do them on their own because only he can see and help them.

It’s not a perfect drama by any means, but it’s pretty cute, and there are many scenes where the paranormal meets the “normal” and the human is the interface!

Oh, I like this prompt, all the endless possibilities and hilarity that usually ensues thanks to it))) It's not the fantasy kdrama without it, honestly, so examples must be MANY.

My top fave would be classic ARANG AND THE MAGISTRATE - FL is a ghost (later an undead with immortal body) and the amount of mental gymnastics ML had to do to cover up for her (and his own ability to see/interact with ghosts) is quite impressive, including making up the excuse for why the two live together ("she's my teacher's daughter he entrusted me to take care of!" - nice try, but no one buys it anyway lol), why she gets mortally wounded on multiple occasions yet never dies, why all her injuries magically disappear, why her corpse remained perfectly fresh for years... There's also this morbidly hilarious moment when he impulsively kisses her in the moment of dying and then tries to save his ass from well-deserved beating by claiming it was resurrection first-aid)))

In My Love From the Star, Lawyer Jang has been helping alien Min-Joon by forging death certificates and creating new identities for him every ten years in order to hide the fact that his appearance never ages.

In Zombie Detective, Sun-Ji discovers that beneath the BB cream, Moo-Young is actually a zombie. After getting over her initial shock and fright (and taking off the protective gear) she helps him hide his identity.

There are a number of examples in which people have to cover for someone who appears normal, but is actually possessed by a ghost or is a victim of body switching. Examples: Ghost Doctor, Oh My Ghost, Mr. Queen.

I don't have anything specific to add; I just want to say I love this trope (is it a trope?), and that this is a great thread😄👍

Im going with the Goblin and his nephew! Then finding out that the “nephew” is actually God. 😆

Not sure if this fits the bill but My Roomate is a Gumiho and Meow: The secret boy.

I dunno if this fits the prompt but I can’t stop thinking about TALE OF THE NINE TAILED 1938. Technically most of the characters are deities and nonhuman, so this probably won’t count but there is a scene where a baby suddenly appears in front of Yeon and Rang. Both of them try to get rid of the baby but the baby keeps appearing in front of them. Later they find out the baby is a lucky baby who others are trying to kidnap. So they decide to keep the baby and it’s so wholesome and sweet seeing both Yeon and Rang parenting the baby. Okay I’ll stop fangirling now 😅

Doom At Your Service has heaps, especially since Doom has a very 'doesn't give a shit' attitude, and so Tak Dong Kyung has her work cut out for her trying to cover for his mannerisms.

In A Korean Odyssey, FL tries to act as there is nothing strange when Son Oh Kong does something magical in presence of her associate.
In Blood, ML's best friend helps him with a false scar to hide his regenerating abilities. (I do not recommend this drama)
In cdrama I Am the Years You Are the Stars, ML does not dies and has guardians to manage his properties and all the administrative tasks of being alive.

Already cited: Zombie detective, Are you humain too, Doom at your service.

There is a drama where ML sometimes has the idea to pretend to be on the phone while talking to the surnatural being only he sees, but I do not want to give the name because that's a big spoiler. What a conudrum.

what was that mermaid series with Jo Boa?

This is one of my favorite genre
Some on my top list
Hotel del luna
Goblin
My Rooommate is a gumiho
Tale of nine tailed 1938
The currently airing Heartbeat
Ghost Doctor if it counts