Many space mission planning problems may be formulated as hybrid optimal control problems (HOCP), i.e. problems that include both real-valued variables and categorical variables. In interplanetary trajectory design problems the categorical variables will typically specify the sequence of planets at which to perform flybys, and the real-valued variables will represent the launch date, flight times between planets, magnitudes and directions of thrust, flyby altitudes, etc. Previous work by these authors addressed the problem of autonomously generating multiple-flyby interplanetary trajectories with impulsive chemical propulsion. This paper extends the authors' previous work to multiple-flyby interplanetary trajectories with low-thrust continuous propulsion. A HOCP framework is constructed with two nested loops - an \outer-loop'to determine the optimal sequence of flybys and an \inner-loop' to find the optimal trajectory for each candidate sequence. An integer genetic algorithm (GA) is used to solve the outer-loop problem, and monotonic basin hopping (MBH) is used to solve the inner-loop problem. The HOCP is demonstrated on a notional Earth-to-Jupiter problem, similar to the now cancelled Jupiter Icy Moons Orbiter, as well as an early version of the BepiColombo mission and a notional Uranus orbiter.