Network interpenetration has been proposed as a mechanism for generating liquidliquid phase transitions in one component systems. We introduce a model of four coordinated particles, which explicitly treats the system as a mixture of two interacting interpenetrating networks that can freely exchange particles. This model can be solved within Wertheims theory for associating fluids and shows liquidliquid phase separations (in addition to the gasliquid) for a wide range of model parameters. We find that originating a liquidliquid transition requires a small degree of interpenetrability and a preference for intranetwork bonding. Physically, these requirements can be seen as controlling the softness of the particleparticle interaction and the bond flexibility, in full agreement with recent findings