Han is our co-protagonist, along with the savvy Dagny Taggart, and our main romantic male lead for much of the novel. (At least until he gets upstaged in Volume 3. Which is a serious bummer for poor Hank.)
Hank might just have the worst life of any character in the novel. His family is awful, his wife is evil, his true love disappears then dumps him for another man, and in the end he has to go live in the same town with said true love and her new boyfriend.
Somehow, though, Hank manages to not come off as a sad-sack Charlie Brown. In fact, the worse he is treated, the more likable he becomes. Perhaps it's because, in a novel filled with a lot of larger-than-life, heroic figures, Hank is someone we can relate to pretty well. We follow his struggles and his personal development from the very beginning of the novel.
Mr. Henry Rearden
Let's start off by assessing Hank's other persona: Henry. Henry Rearden is what people who don't know Hank very well call him, and this group includes businesspeople (not the cool ones) like James Taggart as well as members of Hank's own family. Henry Rearden is blasted in the media for being a greedy industrialist, and he's blasted in his own house for being a workaholic. (And also an evil industrialist.)
His mother, brother, and wife seem to think it's their mission in life to torment Hank. They constantly mock him, scold him, and demand he do things for them. Hank gradually begins to realize that his family is walking all over him and, over the course of the novel, he begins to sever ties with them. This process mirrors the one he goes through in his professional life. His acceptance of "bad" values and his highly misplaced sense of guilt and self-loathing is what keeps him out of Galt's Atlantis for so long. Professionally, he was probably ready to head off to Atlantis long before he actually did it. And that frightens Hank:
Because he felt an exultant desire to laugh – as he had laughed at the news of Wyatt's fire, as he had laughed at the crash of d'Anconia Copper – and knew that if he did, the thing he feared would hold him, would not release him this time, and he would never see his mills again. (18.104.22.168)
The prospect of losing control, and of totally realigning his views and his value system, is frightening. But what exactly is Hank's value system, and why does it cause him so many problems for so long?
This is of course a reference to the bold sign that Hank wanted to hang up when he was riding a wave of euphoria after pouring his first batch of Rearden Metal. Hank's values seem pretty easy to nail down: they are the same as Dagny's, Francisco's, John's, etc. The internal monologues and occasional speeches we get from Hank are evidence:
This is the world and the core of it, this is what made the city – they go together, the angular shapes of the buildings, and the angular lines of a face stripped of everything but purpose – the rising steps of steel and the steps of being intent upon his goal. (22.214.171.124)
Hank believes in hard work, achievement, pride, and honor. But for too long he doesn't realize that his values don't mesh with those of the "looters." For instance, he tries to treat his wife respectfully, when her only goal is to torture him.
Hank's main hang-ups have do with his personal relationships. His resentment of his awful family, his relationship with Dagny, and sex in general cause him a lot of guilt. Francisco confronts Hank about these issues and tries to get him to stop having a massive guilt-complex:
You keep pushing out of your mind the thoughts which you believe to be evil.... You sacrifice your emotions as the first cost of any problem....You are willing to bear anything. (126.96.36.1990)
What if you're placing your virtue in the service of evil and letting it become a tool for the destruction of everything you love, respect, and admire? Why don't you uphold your own code of values among men as you do among iron smelters? (188.8.131.52)
Hank's devotion to his work and his sense of morality and guilt keep him apart from Galt and his strikers for almost the entire book. Interestingly, we barely see Hank in Atlantis. We only get a very brief mention of him at Francisco's house at the very end of the novel. It's almost hard to picture him there, which Dagny comments on during her stay there:
She felt, simultaneously, that Hank Rearden's presence in this valley was impossible – and that this was his place, peculiarly his. (184.108.40.2064)
This is significant: Hank's story is very much one of the outside world. He gradually learns to shed his guilt and finally joins the strike, but the moment he does, his narrative arc effectively ends. This puts Hank in a unique position in the novel: he's nearly the only character whose journey towards the strike we get to follow in full. Hank serves as something of a spotlight on the real world; it's through his personal journey that we learn about the "looters" and their views.
How does he make this journey? Francisco is definitely Hank's major teacher, but he has another source of inspiration as well: Dagny Taggart.
"The girl on the flatcar"
In a climactic scene at the end of Volume 3, Chapter 6, Hank simultaneously realizes that he is in love with Dagny and that he has been serving a corrupt system. In keeping with the novel's themes, Hank's love for Dagny is an expression of his value system, which is also connected to his love of work and life.
Hank is blackmailed by the government into signing over the rights to Rearden Metal, the invention that inspired his proud and joyful "Rearden Life" fantasy. Hank not only realizes how much he loves Dagny here, but also how culpable he is in his own blackmail. If he hadn't been ashamed of his relationship with Dagny, and sought to hide it, the blackmailers would have no leverage:
Now, looking from the memory of the girl on the flatcar [Dagny] to the Gift Certificate lying on his desk, he felt as if the two met in a single shock, fusing all the days and doubts he had lived between them, and, by the glare of the explosion, in a moment's vision of a final sum, he saw the answer to all his questions. His thought: Guilty? – guiltier than I had known, far guiltier than I had thought, that day – guilty of the evil of damning as guilt that which was my best. (220.127.116.11)
But just when Hank comes to this epic realization, he loses Dagny to John Galt. What gives here? Hank is all lined up and ready to go as the book's major romantic hero, then some mystery dude swoops in and steals his thunder in Volume 3. For much of the book, Hank and Dagny are running on parallel tracks, so to speak. Their stories mirror one another, as both struggle to reconcile their personal values to the reality of the world, and to understand the nature of the strike and of John Galt. Their stories overlap for a long time as well. They even team up on the same quests together (building the John Galt Line, hunting for the inventor of the motor).
But just as Hank comes to his major realization, so does Dagny. She understands that she is still hunting for Atlantis and the man who embodies all her values: the as-yet-unnamed John Galt. Dagny's narrative path takes her in a different direction from Hank, which brings their romance to an end. We'll let Hank explain it, since we're actually still kind of miffed on his behalf:
No, you did not make it worse for me, you set me free, you saved us both, you redeemed our past. ... I am happy that I have seen the truth – even if my power of sight is all that's left to me now. (18.104.22.168)
Hank's story really does all boil down to sight. Over the course of his journey, he sees what the looters really are, sees his guilt for what it is, sees his relationship with Dagny in a truer light, and sees, sadly, that his narrative path will have to diverge from Dagny's.