The analysis of dynamic network data based on statistical models has attracted wide attention in social and biological research fields, where the interactions between individuals may undertake large and systematic changes. In this paper, we propose a statistical model for the recurrent events of instantaneous interactions between the nodes, in which a Poisson process with a semiparametric mean function of recurrent interactions is considered under the condition of latent membership of the nodes. A joint model of the recurrent interaction process and discrete-time observation process is proposed to characterize the impact of the time-slices for the snapshots. A variational expectation-maximization algorithm is applied to obtain the estimators of the connectivity parameters and the latent variables. The asymptotic properties of the estimates are also discussed. Some simulation studies and applications on real data are presented to illustrate the performance of the proposed models and methodology.