Discrete-continuous non-linear optimization models are frequently used to formulate problems in Process System Engineering. Major modeling alternatives and solution algorithms include generalized disjunctive programming and MINLP. Both have advantages and drawbacks depending on the problem they are dealing with. In this work, we describe the theory behind LOGMIP, a new computer code for disjunctive programming and MINLP. We discuss a hybrid modeling framework which combines both approaches, allowing binary variables and disjunctions for expressing discrete choices. An extension of the Logic-Based OA algorithm has been implemented to solve the proposed hybrid model. Computational experience is reported on several examples, which are solved with disjunctive, MINLP and hybrid approaches.