Simultaneous optimization of fuel consumption and battery lifetime is addressed in this work. A differential capacity degradation model is used to predict capacity loss, and linear time-varying and nonlinear MPC techniques are used to solve the energy management problem. It is shown that penalizing battery power in the MPC cost function can prolong battery lifetime by about 50 percent while achieving small gains in fuel economy compared to when the cost function only aims to minimize fuel consumption. An analysis of robustness against uncertainties in drive-cycle information shows that the controller is well-behaved and has good performance under uncertainty.