This paper presents a time Petri net (TPN) model with mixed semantics that efficiently addresses the schedulability analysis problem of the existing semantics models. The proposed model associates each firable transition with a mandatory firing point that is set to the least upper bound of the transition and its non-conflicting transitions. This treatment not only eliminates the effect of conflicting transitions on the transition friability and extends the scheduling scope of the TPN model, but also ensures the time limit of the task scheduling. To determine the expressiveness of the mixed model, the study proves that the mixed semantics model has the power of Turing machines and its marking reachability problem is undecidable. The timed expressiveness of three semantics models with respect to timed language acceptance is also compared. A state class approach is then proposed for the scheduling analysis of the mixed model. Finally, a flexible manufacturing system is used as an example to compare the scheduling ability of three semantics models.