Longitudinal semicontinuous data, characterized by repeated measures of a large portion of zeros and continuous positive values, are frequently encountered in many applications including biomedical, epidemiological, and social science studies. Two-part random effects models (TPREM) have been used to investigate the association between such longitudinal semicontinuous data and covariates accounting for the within-subject correlation. The existing TPREM is, however, limited to incorporate a functional covariate, which is often available in a longitudinal study. Moreover, the existing TPREM typically assumes the normality of subject-specific random effects, which can be easily violated when there exists a subgroup structure. In this article, we propose a nonparametric Bayesian functional TPREM to assess the relationship between the longitudinal semicontinuous outcome and various types of covariates including a functional covariate. The proposed model also relaxes the normality assumption for the random effects through a Dirichlet process mixture of normals, which allows for identifying an underlying subgroup structure. The methodology is illustrated through an application to social insurance expenditure data collected by the Korean Welfare Panel Study and a simulation study.