We consider restoring multiple interdependent infrastructure networks after a disaster damages components in them and disrupts the services provided by them. Our particular focus is on interdependent infrastructure restoration where both the operations and the restoration of the infrastructures are linked across systems. We provide new mathematical formulations of restoration interdependencies in order to incorporate them into an interdepedent integrated network design and scheduling (IINDS) problem. The interdependent infrastructure restoration efforts resulting from solving this IINDS problem model a centralized decision-making environment where a single decision-maker controls the resources of all infrastructures. In reality, individual infrastructures often determine their restoration efforts in an independent, decentralized manner with little communication among them. We provide algorithms to model various levels of decentralization in interdependent infrastructure restoration. These algorithms are applied to realistic damage scenarios for interdependent infrastructure systems in order to determine the loss in restoration effectiveness resulting from decentralized decision-making. Our computational tests demonstrate that this loss can be greatly mitigated by having infrastructures share information about their planned restoration efforts.