Solvents strongly affect reaction-based chemical processes. Process design, therefore, needs to integrate solvent design. For this purpose, the integrated computer-aided molecular and process design (CAMPD) method Rx-COSMO-CAMPD is proposed. It employs a hybrid optimization scheme combining a genetic algorithm to explore the molecular design space with gradient-based optimization of the process. To overcome limitations of molecular design based on group-contribution methods, reaction kinetics and thermodynamic properties are predicted using advanced quantum-chemical methods. Rx-COSMO-CAMPD is demonstrated in a case study of a carbamate-cleavage process where promising solvents are designed efficiently. The results show that the integrated solvent and process design with Rx-COSMO-CAMPD outperforms computer-aided molecular design without process optimization in the identification of solvents that enable optimal process performance.