The work presented as part of this dissertation is primarily motivated by a randomized trial for HIV serodiscordant couples. Specifically, the Multisite HIV/STD Prevention Trial for African American Couples is a behavioral modification trial for African American, heterosexual, HIV discordant couples. In this trial, investigators developed and evaluated a couple-based behavioral intervention for reducing risky shared sexual behaviors and collected retrospective outcomes from both partners at baseline and at 3 follow-ups to evaluate the intervention efficacy. As the outcomes refer to the couples' shared sexual behavior, couples' responses are expected to be correlated, and modeling approaches should account for multiple sources of correlation: within-individual over time as well as within-couple both at the same measurement time and at different times. This dissertation details the novel application copulas to modeling dyadic, longitudinal binary data to estimate reliability and efficacy. Copulas have long been analytic tools for modeling multivariate outcomes in other settings. Particularly, we selected a mixture of max-infinitely divisible (max-id) copula because it has a number of attractive analytic features. The dissertation is arranged as follows: Chapter 2 presents a copula-based approach in estimating the reliability of couple self-reported (baseline) outcomes, adjusting for key couple-level baseline covariates; Chapter 3 presents an extension of the max-id copula to model longitudinal (two measurement occasions), binary couples data; Chapter 4 further extends the copula-based model to accommodate more than two repeated measures in a different application examining two clinical depression measures. In this application, we are interested in estimating whether there are differential treatment effects on two different measures of depression, longitudinally. The copula-based modeling approach presented in this dissertation provides a useful tool for investigating complex dependence structures among multivariate outcomes as well as examining covariate effects on the marginal distribution for each outcome. The application of existing statistical methodology to longitudinal, dyad-based trials is an important translational advancement. The methods presented here are easily applied to other studies that involve multivariate outcomes measured repeatedly.