A generalized lattice Boltzmann (LB) model for solving Advection-diffusion (AD) problems of heat and mass transfer in porous medium is proposed. The complicated heat and mass transfer problems in porous media can be regarded as the physical phenomena with different interface conditions between two phases. Three typical interface conditions can be roughly classified based on the continuity of a scaler of Temperature/Concentration and a flux of Heat/Mass for energy and mass conservation equations. By modifying the equilibrium distribution function in the LB model, the effects of variable heat capacity and storage coefficient on heat and mass transfer, respectively, can be easily coupled. In addition, by adding a field parameter counting for the Henry effect for a solute in different solvent, the jump interface condition for the concentration in different phases can be coupled easily in solving the mass conservation equation. Therefore, a generalized LB model for dealing with three typical AD problems is summarized. Finally, two typical AD problems in multiphase systems are calculated to validate the proposed model, the results show that it performs well for solving the typical isotropic and anisotropic AD problems in multiphase systems.