Hao Sun / Abstract : Small area estimation (SAE) is widely used to produce reliable estimates of characteristics of interest such as means,counts, quantiles when there exists some limitations of the available data. In SAE, people usually focus on univarite response with generalized linear mixed model to which allows for additional variability. However, in many cases, we could have bivariate correlated responses and fit GLMM for them together will be very tough. We introduce the joint distribution for bivariate responses (one is continuous and the other is binary), and use Monte Carlo EM algorithem as our model parameter estimation procedure. In addition, we use empirical Bayes predictor to estimate our parameters of interest and compare MSE with other benchmark models. The simulation results shows that our method has more accurate estimation for both model parameters and our parameters of interest. Finally, our future work will also be discussed.