This paper studies the optimal reinsurance and investment problem with consideration of joint interests of an insurer and a reinsurer under the risk model with common shock dependence. Suppose that the surplus process of the insurance company and the reinsurance company is described by the diffusion approximation model, and the insurance company can purchase proportional reinsurance whose reinsurance premium is calculated by the mean-variance premium principle to disperse risks. Both insurance companies and reinsurance companies can invest in risk-free assets and risk assets whose price process follows the square-root factor process. By stochastic control theory, we establish the robust Hamilton-Jacobi-Bellman (HJB) equation and obtain the optimal reinsurance-investment strategies and the corresponding value functions under the objective of maximizing the expected utility of the weighted sum of terminal wealth of insurance companies and reinsurance companies. In addition, we give some numerical examples to illustrate the effects of some model parameters on the optimal reinsurance and investment strategies.