Panel count data often occurs in a long-term recurrent event study, where only the occurrence counts between adjacent observation times are observed. Most traditional methods only handle panel count data for one single event. In this paper, we propose a Bayesian semiparameteric approach to analyze panel count data for two types of events. For each type of event, the proportional mean model is adopted to model the mean count of the event, where its baseline mean function is approximated by the monotone I-splines. The correlation between events are modeled by common frailty terms and a scale parameter. Unlike many frequentist estimating equation methods, our method is based on the observed likelihood and makes no assumption on the relationship between the recurrent process and the observation process. For implementation, we develop an efficient Gibbs sampler based on a novel data augmentation. Simulation studies show good estimation of the baseline mean function and the regression coefficients and the importance of including the scale parameter to flexibly accommodate the correlation between events. Finally, a skin data example is fully analyzed to illustrate the proposed method.