This paper presents a hybrid reconfigurable intelligent surface (RIS) and dynamic metasurface antenna (DMA) assisted multiple-input multiple-output (MIMO) communication system, which is capable to realize massive MIMO technology with superior performance at low hardware implementation cost. We aim for maximizing the achievable ergodic rate of the system through jointly designing the transmit covariance matrix of user, the phase shift matrix of RIS, and the DMA weight matrix at BS only with statistical channel state information. Based on the derived closed-form asymptotic ergodic rate, we first obtain the optimal transmit covariance matrix under the power consumption constraint and specific absorption rate constraints. Then, we obtain a locally optimal phase shift matrix of RIS via the projected gradient ascent algorithm. Finally, we reconfigure the DMA weights by utilizing the optimal solution of the unconstrained DMA problem. Simulation results demonstrate that the proposed optimization algorithm outperforms the baseline.