The interaction of ionizing and far-ultraviolet radiation with the interstellar medium is of great importance. It results in the formation of regions in which the gas is ionized, beyond which are photodissociation regions (PDRs) in which the gas transitions to its atomic and molecular form. Several numerical codes have been implemented to study these two main phases of the interstellar medium either dynamically or chemically. In this paper we present TORUS-3DPDR, a new self-consistent code for treating the chemistry of three-dimensional photoionization and photodissociation regions. It is an integrated code coupling the two codes TORUS, a hydrodynamics and Monte Carlo radiation transport code, and 3D-PDR, a photodissociation regions code. The new code uses a Monte Carlo radiative transfer scheme to account for the propagation of the ionizing radiation including the diffusive component as well as a ray-tracing scheme based on the HEALPix package in order to account for the escape probability and column density calculations. Here, we present the numerical techniques we followed and we show the capabilities of the new code in modelling three-dimensional objects including single or multiple sources. We discuss the effects introduced by the diffusive component of the UV field in determining the thermal balance of PDRs as well as the effects introduced by a multiple sources treatment of the radiation field. We find that diffuse radiation can positively contribute to the formation of CO. With this new code, three-dimensional synthetic observations for the major cooling lines are possible, for making feasible a detailed comparison between hydrodynamical simulations and observations. ; Comment: 17 pages, 10 Figures, accepted for publication in MNRAS. Comments welcome