The functioning of infrastructure networks is vital for modern communities. Maintenance should be planned to ensure infrastructure's functionality and safety at the lowest cost. Interconnected infrastructure networks can affect each other's functionality, and maintenance on one network can impact the serviceability of others. Planned intervention grouping across infrastructures reduces set-up costs and service interruption, improving infrastructure availability and serviceability at lower costs. Finding the best grouping strategy is a known NP-hard problem, with several optimization strategies have been proposed, mainly based on nonlinear models which are computationally expensive and do not guarantee scalability. Furthermore, infrastructure intervention planning models mostly focus on grouping of interventions which are considered as given. In this paper, we propose a new efficient optimization model to optimize intervention grouping for interconnected infrastructure networks. We develop a scalable two-step optimization model where we first plan each individual intervention type based on a preventive maintenance policy accounting for the degradation behavior of objects, then group interventions to minimize the net costs, considering dependencies within and accross infrastructure networks. We formulate the grouping problem as an Integer Linear Program, which can be solved exactly with standard solvers. The model accounts for interactions between infrastructure networks and considers the impact on all stakeholders. It also accommodates various intervention types like maintenance, removal, and upgrading. Using a demonstrative application, we show that our model significantly reduces net costs and outperforms alternative nonlinear formulations and related heuristics in terms of both solution quality and computation performance. Additionally, the optimal intervention plan shows repetitive patterns, which suggests that a rolling horizon strategy could be used where the optimization problem is solved for shorter time horizons, leading to significant computational benefits.