Motivated by a migraine study, we are interested in jointly modeling migraine frequency and duration outcomes collected repeatedly from patients by specialists to investigate the mechanisms of migraine over time. In this motivating longitudinal study, at each hospital visit, the migraineurs were asked to report number of days with migraine attacks they have had within past 30 days and average duration of the attacks. While the frequency outcome is a count variable bounded by 30 days, the duration outcome is completely reported in discrete hours, including 0 for non-migraine days, resulting in a count variable. Furthermore, this bivariate longitudinal count data has an unbalanced structure with irregularly spaced time points due to that each patient visited the hospital with varying number of times within irregular intervals. In this study, we propose a bivariate generalized linear mixed-effects model to jointly analyze the two longitudinal count outcomes within Bayesian framework. We investigate performance of the proposed joint model via a Monte Carlo simulation study and compare its performance with separate models, where each longitudinal count outcome is modeled individually.