The final episode of Season 3 is about as bleak as one can make it. There are two focuses. The first, of course, is the Iowa Caucuses and Franks final push to gain that state, the jumping off point for all presidential candidates. Claire, who really is his equal, is left smiling and schmoozing, in his shadow. I guess that's the way it has to be. As Frank says later, "There is only one chair behind this desk." Frank gets openly meaner and meaner as time goes along. The two of them start to exude a kind of marital frenzy. All Frank's talk about their love fore each other is claptrap; it's about what's best for him.
The second focus is Doug, carrying out his mission to find Rachel. He goes to Venezuela and hunts down Gavin, whom he nearly beats to death. Gavin gives him access to Rachel's information and off he goes. Doug is psychotic; Doug has no conscience. The final scene with Rachel gives him one last chance to be a human being. He really is not.
Of course, the final scene in the last episode sets the stage for some really interesting stuff to take place when Season 4 commences.