Three times a month, Mohammad al-Kirayfawai hands $300 to fighters from the Islamic State for the privilege of driving his refrigerated truck full of ice cream and other perishables from Jordan to a part of Iraq where the militants are firmly in charge.

The fighters who man the border post treat the payment as an import duty, not a bribe. They even provide a stamped receipt, with the logo and seal of the Islamic State, that Mr. Kirayfawai, 38, needs for passing through other checkpoints on his delivery route.

Refuse to pay and the facade of normality quickly falls away. “If I do not,” Mr. Kirayfawai explained, “they either arrest me or burn my truck.”

Across wide expanses of Syria and Iraq, the Islamic State, with the goal of building a credible government, has set up a predatory and violent bureaucracy that wrings every last American dollar, Iraqi dinar and Syrian pound it can from those who live under its control or pass through its territory.