Influenza infections often predispose individuals to consecutive bacterial infections. Both during seasonal and pandemic influenza outbreaks, morbidity and mortality due to secondary bacterial infections can be substantial. With the help of a mathematical model, we investigate the potential impact of such bacterial infections during an influenza pandemic, and we analyze how antiviral and antibacterial treatment or prophylaxis affect morbidity and mortality. We consider different scenarios for the spread of bacteria, the emergence of antiviral resistance, and different levels of severity for influenza infections (1918-like and 2009-like). We find that while antibacterial intervention strategies are unlikely to play an important role in reducing the overall number of cases, such interventions can lead to a significant reduction in mortality and in the number of bacterial infections. Antibacterial interventions become even more important if one considers the--very likely--scenario that during a pandemic outbreak, influenza strains resistant to antivirals emerge. Overall, our study suggests that pandemic preparedness plans should consider intervention strategies based on antibacterial treatment or prophylaxis through drugs or vaccines as part of the overall control strategy. A major caveat for our results is the lack of data that would allow precise estimation of many of the model parameters. As our results show, this leads to very large uncertainty in model outcomes. As we discuss, precise assessment of the impact of antibacterial strategies during an influenza pandemic will require the collection of further data to better estimate key parameters, especially those related to the bacterial infections and the impact of antibacterial intervention strategies.