A new family of Markov Processes called "Markov Interactive Processes" (MIP) is introduced, where several jump components occur in one component at a time with transition rates for each to depend on current states of remaining components. A product-form transient and stationary distributions were obtained under given conditions. Several standard models including Jackson Networks and Markov Modulated Processes become special cases. Approximations for these processes are also provided. New queuing models have been identified to fit the structure of MIP's, and a new family of Markov Processes whose state spaces are partitioned into subspaces where one is "central" and the others where states cannot jump into other subspaces except through the central subspace states.