This paper proposes a dynamic integrated electricity and gas investment (DIEGI) model based on multi-objective optimization concepts that can capture uncertainty in both hydro conditions (i.e. inflows) and demand growth. Thus, our model can determine efficient and adequate electricity and natural gas infrastructure that can deal with hydro conditions driven by extreme natural hazards (e.g. drought), and it also considers the risk of stranded assets in future periods when demand growth is less than expected (both hydro conditions and demand growth can be extremely volatile in countries such as Colombia, Brazil, Chile and Peru). Our multi-objective approach allows regulators and policy-makers to determine not only the least investment and operational cost solution, but also an array of investment portfolios that are Pareto efficient when considering budget constraints (that is the case in some developing countries). Through a case of study, we demonstrate that gas infrastructure plays a critical role in cost and reliability levels of the electricity infrastructure, and that integrated electricity and gas planning can significantly improve the robustness of the combined energy infrastructure to face uncertain scenarios in terms of demand and hydro inflows.