We don't learn much about Aunt Larisa's husband. Sasha thinks of him in terms of "that jerk" (10.2), and he is fairly jerky. He laughs a "nasty laugh" when Sasha claims that Stalin will soon discover that he's made a mistake in arresting his father (9.9), and manhandles Sasha a bit as he makes it clear Sasha will not be allowed to stay at their place:
He leans forward and drives his finger into my chest. "Don't aggravate us, kid. Get lost." And he shuts the door. (9.13)
Clearly, Aunt Larisa's husband is rather cynical (he doesn't blindly accept that the system is all it's propped up to be, like Sasha does), and is only concerned with protecting himself and his immediate family. That's a good way to survive, but it's a terrible way to be a person.