In many clinical studies, multiple longitudinal non-survival responses are recorded simultaneously with a single event time or multiple competing event responses on each study subject. Naturally, these two types of outcomes may be correlated because they are observed from the same individual. To understand this association, a common approach is to model jointly hierarchical generalized linear models (HGLM) and frailty models (unobserved random effects). We propose a joint parametric modeling framework that accounts for the intrinsic association via shared random effects. A single parameter Weibull distribution, whose distribution is appropriate for the analysis of datasets with fewer events, is used. We relax the normality assumption on the distribution of the shared random effects. For inference, the hierarchical likelihood (h-likelihood), which is an efficient fitting procedure, is used to avoid complex integrations. A numerical study is conducted to illustrate the performance of the proposed method and a data example is shown.