Management of fisheries for sustainability requires dealing with multiple and often conflicting objectives. A stochastic viability approach is proposed to address the trade-offs associated with balancing ecological, economic and social objectives in regulating mixed fisheries, taking into account the complexity and uncertainty of the dynamic interactions which characterize such fisheries. We focus on the demersal fishery in the Bay of Biscay and more specifically on the fleets harvesting Norway Lobster (Nephrops norvegicus), Hake (Merluccius merluccius) and Sole (Solea solea). A bio-economic multi-species and multi-fleet model with technical interactions is developed to examine the trade-offs between preserving Spawning Stock Biomass (SSB) of every species and maintaining the economic profitability of the various fishing fleets. Different management strategies are tested and compared. Results suggest that ensuring viability of this demersal fishery requires a significant decrease in fishing capacity as compared to the reference year. The simulations allow comparing the trade-offs associated with different allocations of this decrease across fleets.