Sasha's dad is a big hero, and works as a State Security agent at Lubyanka prison (3.1). This means he's basically a super secret member of the super secret Soviet police who knows a lot of super secret secrets about other super secret people.
We know he's good at his job because Stalin himself supposedly described him as "an iron broom purging the vermin from out midst" (3.1). This later takes on a much more ominous tone when we find out that he sold out his own wife (yes—that would be Sasha's mom) as a foreign spy. Sasha doesn't know this until much later in the book, though, so for most of the novel, he pretty much worships the ground his dad walks on. He wants to be just like him "more than anything" (1.1).
But that might not be such a good idea. We first get the sense that Sasha's dad isn't exactly sunshine and rainbows when Sasha describes how the folks in their shared apartment treat him:
Everyone in the kitchen stops talking when my dad comes in. They look like they are afraid, but I know they are just respectful. (4.1)
This classic moment of cluelessness on Sasha's part reveals a ton about his old man. Sure, being the good, potential Young Soviet Pioneer that he is, Sasha wants to believe the best about his dad. But it's probably pretty clear to the keen readers among us that Sasha's dad doesn't command respect here—he really does inspire fear. And you'd probably be scared, too, if you knew this guy had the power to haul you off to prison at a second's notice for any number of trumped up charges (which is just how State Security rolls). Which of course hints at Sasha's dad's eventual arrest. We never learn about his supposed crimes, but the truth is, it doesn't really matter if he's a good guy or a bad guy. The secret police don't need a reason to haul your butt to jail.
Even though he inspires fear in his neighbors and gets thrown in jail, we can tell he's not a totally bad dude. For example, after Sasha's mom went away, his dad got them a "little Primus stove" to use in their room to warm up food, and he gave the Stukachov family their burner on the communal stove (7.2). Sasha points out that the Stukachovs "needed it more" since they "had so many dependents to feed" (7.2). He probably got this explanation from his dad, so there's definitely some shred of kindness in the guy.
So the question is, how do we square the nice neighbor with the sneaky snitch? The fact that Sasha's dad turned his wife in as a traitor to the Soviet cause is ten kinds of awful, no matter which way you look at it. Sure, he at least had the decency to look "guilty" (or so Aunt Larisa says) after he returned from taking Sasha's mom to the so-called hospital (10.2), but at the end of the day, he still did it, and that's so very not cool.
To be fair, though, he probably didn't have much of a choice. Maybe he's just trying to do the best he can to survive in this environment of rampant accusations and paranoia. If he had stuck his neck out for his wife, he and Sasha might not have made it through the ordeal. No matter which way you slice it, it's clear this guy has had to make some tough calls in his life—decisions we're not quite prepared to understand.
Ah, but Shmoopers, he still had a choice. He could have defended his family, and stood up to authority, no matter the cost. Which is exactly what Sasha does when he decides not to become a snitch, himself. When Sasha decides to stand up for what's right, we can see that, despite the fact he really wanted to be just like his dad at the beginning of the novel, he's going to grow into his own man—one that just might be even better than his father.