With the development of the power distribution Internet of Things (IoT), the escalating power demand of data centers (DCs) poses a formidable challenge to the operation of distribution networks (DNs). To address this, the present study considers the operational flexibility of DCs and its impact on DNs and constructs a collaborative planning framework of DCs, renewable energy sources (RESs), and DNs. This framework employs the interval optimization method to mitigate uncertainties associated with RES output, wholesale market prices, carbon emission factors, power demand, and workloads, and the collaborative planning model is transformed into an interval optimization problem (IOP). On this basis, a novel hybrid solution method is developed to solve the IOP, where an interval order relation and interval possibility method are employed to transform the IOP into a deterministic optimization problem, and an improved integrated particle swarm optimization algorithm and gravitational search algorithm (IIPSOA-GSA) is presented to solve it. Finally, the proposed planning framework and solution algorithm are directly integrated into an actual integrated system with a distribution network and DC to verify the effectiveness of the proposed method.