Behavioral epidemiology, the field aiming to determine the impact of individual behavior on the spread of an epidemic, has gained increased recognition during the last few decades. Behavioral changes due to the development of symptoms have been studied in mono-infections. However, in reality, multiple infections are circulating within the same time period and behavioral changes resulting from contraction of one of the diseases affect the dynamics of the other. The present study aims at assessing the effect of home isolation on the joint dynamics of two infectious diseases, including co-infection, assuming that the two diseases do not confer cross-immunity. We use an age- and time- structured co-infection model based on partial differential equations. Social contact matrices, describing different mixing patterns of symptomatic and asymptomatic individuals are incorporated into the calculation of the age- and time-specific marginal forces of infection. Two scenarios are simulated, assuming that one of the diseases has more severe symptoms than the other. In the first scenario, people stay only at home when having symptoms of the most severe disease. In the second scenario, twice as many people stay at home when having symptoms of the most severe disease than when having symptoms of the other disease. The results show that the impact of home isolation on the joint dynamics of two infectious diseases depends on the epidemiological parameters and properties of the diseases (e.g., basic reproduction number, symptom severity). In case both diseases have a low to moderate basic reproduction number, and there is no home isolation for the less severe disease, the final size of the less severe disease increases with the proportion of symptomatic cases of the most severe disease staying at home, after an initial decrease. This counterintuitive result could be explained by a shift in the peak time of infection of the disease with the most severe symptoms, resulting in a smaller number of people with less contacts at the peak time of the other infection. When twice as many people stay at home when having symptoms of the most severe disease than when having symptoms of the other disease, increasing the proportion staying at home always reduces the final size of both diseases, and the number of co-infections. In conclusion, when providing advise if people should stay at home in the context of two or more co-circulating diseases, one has to take into account epidemiological parameters and symptom severity.