Adopting joint modeling methods for different outcomes is crucial to gain insight from high-dimensional correlated data. Considering this type of data leads to two key challenges: the relationship between different outcomes, and the effects of any possible covariates on each outcome. To meet these challenges, the bivariate probit model is frequently used to assess the correlation between the two outcomes by imposing joint normality. Winkelmann (2012) developed the probit copula model that allows the correlation between two outcomes without imposing joint normality. However, this last approach does not consider the complex relationship between the covariates and the outcome assessed by modeling the conditional quantile function of response variable. We develop the Quantile Probit Copula model, a new joint modeling approach that combines binary quantile regression with a copula probit model. Our model is able to capture the association between the outcomes, and their full distribution by modeling the conditional quantiles. We assess the operating characteristics of our method by means of simulations, and we present an application to the Fragile Families Study.