Abstract: This paper analyzes the optimal density and power allocation for the D2D (Device-to-Device) communication in heterogeneous networks on multi-bands with target of maximizing the D2D transmission capacity. The heterogeneous networks contain one or several cellular systems, and the D2D communication shares uplink resources with them. By utilizing stochastic geometry, it is formed as a sum capacity optimization problem for the D2D network with constraints that guarantee outage probabilities of both cellular and the D2D transmissions. Since the original problem is non-convex, the proof work is divided into two steps: first, it is proved that the power allocation problem is convex when the D2D density is fixed, which can be solved by Lagrangian method; and then that the feasible region for the D2D user density is divided into finite sub-intervals by the outage constraints and the local maximum D2D transmission capacity can be obtained by the derivative method. A sub-interval linear searching algorithm based on the above conclusions is proposed. The simulation results demonstrate the effectiveness of the proposed algorithm and show that the optimal parameters of the D2D transmission is mainly affected by the outage constraints and the interference from cellular systems.