FALLUJA, Iraq — In the days leading up to the storming of Falluja by Iraqi forces, Brig. Gen. Hadi Razaij, the leading Sunni police commander in the campaign, sat on a cot in an abandoned house near the front line. He described the resistance that lay ahead: a determined force of hundreds of jihadists that had months to prepare.

General Razaij’s presence on the battlefield shows that local Sunnis, and not just the Shiite forces that now dominate Iraqi politics, are fighting to liberate their own communities, and has helped tamp down fears that the battle for Falluja would heighten sectarian tensions.

He was dispassionate as he described the challenges, but for him the fight was personal, too. General Razaij’s brother stands accused of being a member of the Islamic State and is in a prison cell after being arrested at a checkpoint with a car full of explosives.

In northern Iraq, Nofal Hammadi, the governor-in-exile of Mosul, is working with the United States to plan for that city’s liberation from the Islamic State. He, too, has family in the fight: Mr. Hammadi’s brother is an Islamic State official, having appeared in a video pledging his allegiance to the terror group and disowning his brother.