This article studies the complete targets coverage problem in a novel and practical context: sensor nodes operating in an Internet of Things (IoT) network that have a dual-battery system with nonideal properties. Specifically, sensor nodes have batteries that cannot be charged and discharged simultaneously. Also, sensor nodes must fully discharge/charge a battery before it is charged/discharged again. We outline a mixed-integer linear program (MILP) and use it to optimize the activation schedule of sensor nodes. Its objective is to maximize complete targets coverage lifetime. We also propose a heuristic solution named battery switching aware algorithm (BSAA) to solve large problem instances. Simulation results show the performance of BSAA achieves approximately 98% of the coverage lifetime of MILP. In addition, equipping sensor nodes with a dual battery system prolongs the coverage lifetime by up to 70.2%.