The analysis of discrete mixed responses is an important statistical issue in various sciences. Ordinal and overdispersed binomial variables are discrete. Overdispersed binomial data are a sum of correlated Bernoulli experiments with equal success probabilities. In this paper, a joint model with random effects is proposed for analyzing mixed overdispersed binomial and ordinal longitudinal responses. In this model, we assume an overdispersed binomial response variable follows Beta-Binomial distribution and use a latent variable approach for modeling the ordinal response variable. Also, the model parameters are estimated via the Maximum Likelihood method, and the estimates are evaluated with a simulation study via the Monte Carlo method. Finally, an application of the proposed model to real data is introduced.