When applying a point process to a real-world problem, an appropriate intensity function model should be designed based on physical and mathematical prior knowledge. Recently, a fully trainable deep learning–based approach has been developed for temporal point processes. In this approach, a cumulative hazard function (CHF) capable of systematic computation of adaptive intensity function is modeled in a data-driven manner. However, in this approach, although many applications of point processes generate various kinds of information such as location, magnitude, and depth, the mark information of events is not considered. To overcome this limitation, we propose a fully trainable marked point process method for modeling decomposed CHFs for time and mark prediction using multistream deep neural networks. We demonstrate the effectiveness of the proposed method through experiments with synthetic and real-world event data.