Marked temporal point processes (MTPP) have emerged as a powerful framework to model the underlying generative mechanism of asynchronous events localized in continuous time. Most existing models and inference methods in MTPP framework consider only the complete observation scenario i.e. the event sequence being modeled is completely observed with no missing events – an ideal setting barely encountered in practice. A recent line of work which considers missing events uses supervised learning techniques which require a missing or observed label for each event. In this work, we provide a novel unsupervised model and inference method for MTPPs in presence of missing events. We first model the generative processes of observed events and missing events using two MTPPs, where the missing events are represented as latent random variables. Then we devise an unsupervised training method that jointly learns both the MTPPs by means of variational inference. Experiments with real datasets show that our modeling and inference frameworks can effectively impute the missing data among the observed events, which in turn enhances its predictive prowess.