Short and a little disjointed because I do not go here™ and am trying to keep the characters consistent with what I've seen. Sorry if it's OOC. It's not all that romantic, whoops.
Dante Sparda x Commandant
Doomed by the narrative, which is quite unfortunate as the two of you make a dynamic duo. You play the straight man to his goofy persona with sarcastic quips sharp enough to rival Lucia's blade. On the battlefield, you work together flawlessly: a match made in hell for whomever your poor opponents are. You typically play strategist and look for openings and weak spots while he dances across the battlefield with the grace and brutality of a tiger. You move in sync with each other, and hardly find it necessary to consciously reposition yourselves to be in the constantly shifting "optimal area."
From first contact up until the mirror demon's defeat, the two of you slowly grew from workplace acquaintances to friendly coworkers. It was during the months of "down time" afterwards that your relationship truly blossomed. The corrupted, ascendants, hetero creatures, etc. seemed to be far less active than previously, so field missions became far more sparse and you ended up spending most of you time "on-the-clock" catching up on the mountain of paperwork you hadn't had the chance to get to. Occasionally Dante would wander into your office and you'd use the opportunity to slack off extract more information about this strange alternate world.
It starts off general: food, drink, housing, extracurricular activities, and the like. You don't typically enjoy the finer dinning establishments Babylonia has to offer due to time constraints, so your end of the conversation is quite lacking. The two of you decide to go on a restaurant adventure while Dante's still around to remedy this awful fact. You have to admit the look on one particular waiter's face was priceless when you told him that the strawberry sundae was for "the gentleman sitting next to [you], actually."
The two of you bond over your similar "protector of humanity" roles. Though neither of you serves as the sole protector of humanity, it appears that both of you have become somewhat of a figurehead that rallies the spirits of both allies and civilians. Sometimes it seems like you're treated as the Deus Ex Machina that will magically fix everything when everything goes to pot. It's a lot of pressure to put on one person, especially when you feel as though you have no peers that could empathize with your plight.
He's a little jealous of your team. You've got so many folks you're close with that can trust and protect you as well as you do for them. He's got many friendly folks, but only a handful he's... Somewhat close with (and who's fault is that hmm?). Really, at this current juncture in life, the only person he has that's a constant presence and like your construct friends is, well, you. He's got Vergil for now, but he's well aware that that will most likely not be the case when he gets back, and it's not like the two are attached at the hip even now, as it is.
When he's finally able to go home, he will do so almost immediately. Duty calls, something the two of you are deeply familiar with. He will wish you well, and hope that your paths will cross again one day.
Perhaps one day, if you ever beat the odds and save your world, you'll see a familiar portal. Then you and potentially the rest of the Gray Raven squad will fade into mythological status as heroes who showed up during humanity's darkest hour and vanished after saving the world to go help another world in a similar yet terribly different situation. Maybe there will be a new figure or four showing up to humanity's aid by the side of a certain son of Sparda.
Vergil Sparda x Commandant (ft. Adopted Daughter Alpha)
He stays lol. Thanks to her contribution (plus the exponentially decreasing threat the ascendants pose to humanity thanks in large part to a certain someone fraternizing with the enemy and giving Hassen and Nikolai dual migraines with all the court martials) Alpha is allowed to be in Babylonia, albeit under heavy surveillance.
The three of you often run missions together, sometimes with the rest of the Gray Raven squad, and sometimes alone. You're all dangerous in your own right (as a certain demon could probably testify to if he wasn't busy being very dead), but you also have your own strengths. As an ascendant and as a half demon, Alpha and Vergil are completely immune to the Punishing Virus, making it easy for them to go all out when on the offensive. As natives to this world, you and Alpha have a better grasp on geography, secret codes, and politics of certain areas. As non-ascendants, you and Vergil generally have an easier time when having to interact with various troops, civilians, and people in positions of power.
You meet up with them in quiet lulls between paperwork and missions as well. You haven't interacted as much with Vergil as you had with Dante during their chaotic entrance into this world thanks to chance and a multitude of other factors. You would very much like to change this fact. You also want to check up on Alpha and make sure she's doing alright in an old place that contains few fond memories. Sometimes you meet up with both of them, and sometimes it's just two of you together.
The three of you are quite used to entertaining wild and bombastic personalities, so it's refreshing to be in the presence of others that just let you be and breathe. Some days are spent on the training grounds sparring with each other, and other find you meandering through a sparsely populated mall or garden as you chat about interests, happenings, and other little nothings. One day, Alpha brought her motorcycle into the workshop and gave you two a rundown on what special modifications she made along with giving the two of you a little show. Another day, you all went to a book store (and all ended up buying something).
Alpha's not too interested in literature, at least, not to the degree you and Vergil are. As such, the two of you have formed a bit of an informal book club making use of the access you have to golden age records. You're a bit surprised at how well he's able to pick apart and break down various themes and leitmotifs.
Unfortunately, the scientists at Babylonia manage to get a workable portal from blueprint into reality and your days must come to an end. You don't see Vergil that night. Alpha disappears the next morning. You go to say your goodbyes to the Sparda twins as Vergil swings Yamato to open up a way home. Vergil turns, stuffs a folder full of papers into Dante's arms that he had been hiding under his jacket, and shoves him through the portal. He then turns and walks out of the room, seemingly uncaring about the shocked looks sent his direction.
Dante has too many important reasons to get back to his original world. Vergil? Not as many, especially after giving Dante a copy of the blueprints used to construct the portal stabilizer that Babylonia synthesized. Vergil has a few individuals (Dante included) that would tie him to his original world, and if they were able to visit (or stay permanently) he'd have no issues staying here. He's aware that his brother is quite clever and reliable despite his personality and would likely be able to reconstruct the portal base with... relative ... ease. Within a few years at most, hopefully. The materials used are shared between both worlds, so there at least shouldn't be an issue there.
Since the original one way portal was capable of linking the two worlds, it makes sense to assume that having another portal in the other world that's tuned to the frequency of this world as well as it's own will likely sync up with the portal frame from this world, providing safe (enough) transport to a controlled environment. As for it needing Yamato's power to work, well, he's willing open the portal on this side of the world once a day every day until it finally syncs (He's a Sparda, and apparently Sparda's are very headstrong and stubborn when they want to be).
While he waits, life somewhat returns to normal. Missions, leisure time, a visit with Alpha (and Luna, he was surprised to learn that Alpha has a little sister) planned.... Dinner out with you.