Sexually-transmitted disease (STD) transmission in a population depends on the underlying sexual network of that population. It is known that sexual behavior is heterogeneous and partially assortative, so informative models need to account for these complex attributes. We present a model of the transmission of bacterial STDs. This 3-disease SIS model describes the behavior of chlamydia, gonorrhea, and syphilis with coinfections and universal recovery in a fixed population. First, we assume homogeneous mixing and homogeneous sexual behavior in an 8-equation ODE model, with equations for each coinfection states. We study its equilibria, particularly emphasizing the behavior of the total prevalence of each disease with respect to the behavior of the ODE model. We then extend the ODE model by incorporating a time-dependent network structure. We examine the prevalence of each disease for both models, which we compare to determine the effects of increased complexity on forecasts of disease prevalence.