Most travel behavior studies on route and mode choice focus only on an individual level. This paper adopts the concept of multi-state supernetworks to model the two-person joint travel problem (JTP). Travel is differentiated in terms of activity-vehicle-joint states, i.e. travel separately or jointly with which transport mode and with which activities conducted. In each state, route choice can be addressed given the state information and travel preference parameters. The joint travel pattern space is represented as a multi-state supernetwork, which is constructed by assigning the individual and joint networks to all possible states and connecting them via transfer links at joints where individuals can meet or depart. Besides route choice, the choices of where and when to meet, and which transport mode(s) to use can all be explicitly represented in a consistent fashion. A joint path through the supernetwork corresponds to a specific joint travel pattern. Then, JTP is reduced to an optimization problem to find the joint path with the minimum disutility. Three standard shortest path algorithm variants are proposed to find the optimal under different scenarios. The proposed framework further indicates the feasibility of multi-state supernetworks for addressing high dimensional problems and contributes to the design of a next generation of joint routing systems.