Hybrid manufacturing technology has enabled manufacturers to combine advantages of mainly subtractive and additive manufacturing technologies. A single machine supports producing products with complex geometry, at high quality, and with a high degree of automation. To benefit from these advantages, decisions taken in the process planning stage of such a sophisticated manufacturing system should be optimized. The objective of this paper is to determine the optimal process plan considering both the engineering and manufacturing aspects of the hybrid technology. A comprehensive process planning model is proposed. The model specifies the optimal sequence of additive and subtractive features that minimizes the production cycle time. In addition, the model sets the optimal part orientations such that the time needed for building support structures, performing post-processing and inspection operations, changing cutting tools and printing nozzles, and unclamping the part is minimized. The model is comprehensive as it considers productive and non-productive times, precedence, technological, quality, and manufacturing restrictions imposed on hybrid manufacturing systems. The proposed model is nonlinear; due to this nonlinearity, the model is intractable. A linearization scheme is applied to formulate an equivalent linear model that is solvable to optimality by commercial solvers. Case studies on test and industrial parts are provided to evaluate the computational performance of the proposed model. Integrating the proposed model in hybrid manufacturing (HM) systems ensures adopting the HM technology in its optimal direction. HM technology is an enabler of establishing a smart manufacturing system which is one of the pillars of Industry 4.0.