We present a real-time optimization framework to manage Hybrid Residential Electrical Systems (HRES) with multiple Energy sources and heterogeneous storage units. HRES represents urban buildings where photovoltaic (PV) or other renewable sources are installed along with the traditional connection to the main grid. In this paper heterogeneous storage units are used to realize energy buffers for the exceeding energy produced by the renewable when buildings and the grid are not available to accept it. We considered two different battery banks as electric energy storage, in particular lead-acid as the primary one for its low price and low self-discharge rate; while the lithium-ion chemistry is used as secondary bank because of the higher energy density and higher number of cycles. The proposed optimization strategy aims at maximizing the lifetime of the battery banks and to reduce the energy bill by managing the variability of the PV source, in price-varying scenarios. We used a Dynamic-Programming (DP) algorithm to schedule off-line the use of the lead-acid bank minimizing the number of cycles and the Depth-of-Discharge (DoD) under given irradiance forecasts and user load profiles. Forecasts of the user loads and of the renewable energy intake are introduced in the optimization. Moreover a Real-Time scheme is introduced to manage the lithium bank and to minimize the need and the purchase of energy from the Grid when the actual demand does not fit the forecast. Our simulation results outperform the state of the art where the efficiency of both banks is not taken into consideration, even if complex approaches based on DP are used.