The Chief lost his job because he took the blame because she was trying to save his wife and him.

She knows she was wrong, she's the first person to say so and try to keep everyone else out of it. Doesn't mean her husband should treat her like crap. When Derek's having problems at work she's always there for him despite him treating her like crap.

Like when he killed that pregnant wife (Jon Hamm's girlfriend) and he flipped out and quit.