Few previous works integrated both uncertainty and environment disruption into traffic network design problems (NDPs). This study aims to address this gap. First, the mathematical framework of the strategic user equilibrium (StrUE) traffic assignment under volatility of both total travel demand and link capacity is analyzed. Second, we incorporate the StrUE traffic assignment into a network design project and propose a multi-objective bi-level NDP program. Two objective functions are formulated, which are respectively to minimize the expected total system travel time and minimize the expected total system off-gas emissions under StrUE. Third, we develop two tailored solution methods–an enumerative algorithm and a metaheuristic method based on a genetic algorithm. Finally, systematic evaluation of the performance of the proposed approach is conducted. The results highlight that ignoring uncertainty considerations can result in sub-optimal design solutions in terms of expected network performance. Also, the two objectives, to minimize system-level travel time and vehicle emission, are conflicting for certain design scenarios.