One of the most important goals of green logistics is to reduce the destructive side effects of freight transportation which can lead to several types of health risks. The pollution routing problem (PRP) is an extension of the vehicle routing problem (VRP) which considers greenhouse gas emission in addition to the travel time, cost, and delivery constraints. Another environmental impact of vehicles, especially in urban areas is noise emission which is ignored in optimization PRP researches. This form of pollution endangers physical well-being by causing annoyance, hearing loss, heart disease, mental issues for children, and sleep disorders. In this paper, using noise emission mathematical equations, we aim to reduce noise and exhaust gas emission in VRP with a heterogeneous vehicle fleet and respect to budget, and time window constraints. Moreover, a new hybrid robust-stochastic optimization approach is developed which can address interval uncertainty of parameters in each individual uncertainty scenario. This model suggests a range of solutions that can be selected according to decision maker conservatism level and preferences. To examine the performance of the model, a real-world data sets from PRPLIB instances are adopted. The results approve the possibility of finding a sustainable solution for VRP which takes into account various aspects including fuel consumption, and noise emission simultaneously.