Co-pyrolysis is considered a very promising technology for the treatment of solid wastes as it can rapidly realize the volume reduction of raw materials and obtain high value-added products. To realize the resource utilization of newly emerging solid wastes in relation to edible fungi residue and waste plastics, mushroom residue (MR), a representative of edible fungi residue, was co-pyrolyzed with waste plastic bags (PE), waste plastic lunch boxes (PP), and waste plastic bottles (PET). The thermal behavior and pyrolysis kinetics of the mixtures were investigated. It was found that the softening of the plastics in the mixtures led to an increase in the initial pyrolysis temperature of MR by 2–27 °C, while the pyrolytic intermediates of MR could greatly promote the decomposition of the plastics, resulting in a decrease in the initial pyrolysis temperatures of PE, PP, and PET in the mixtures by 25, 8, and 16 °C, respectively. The mixture of MR and PE (MR/PE) under different mixture ratios showed good synergies, causing the pyrolysis peaks attributed to MR and PE to both move towards the lower temperature region relative to those of individual samples. The increase in heating rate led to enhanced thermal hysteresis of the reaction between MR and PE. The strength of the interaction between plastics and MR based on mass variation was subject to the order PE > PP > PET. The pyrolysis activation energies of MR, PE, PP, and PET calculated from kinetic analysis were 6.18, 119.05, 84.30, and 74.38 kJ/mol, respectively. The activation energies assigned to MR and plastics were both reduced as plastics were introduced to co-pyrolyze with MR, indicating that MR and plastics have a good interaction in the co-pyrolysis process. This study provides theoretical and experimental guidance for the resource utilization of agricultural solid wastes via thermochemical conversion.