This work presents new secondary regulators for current sharing and voltage balancing in DC microgrids, composed of distributed generation units, dynamic RLC lines, and nonlinear ZIP (constant impedance, constant current, and constant power) loads. The proposed controllers sit atop a primary voltage control layer, and utilize information exchanged over a communication network to take necessary control actions. We deduce sufficient conditions for the existence and uniqueness of an equilibrium point, and show that the desired objectives are attained in steady state. Our control design only requires the knowledge of local parameters of the generation units, facilitating plug-and-play operations. We provide a voltage stability analysis, and illustrate the performance and robustness of our designs via simulations. All results hold for arbitrary, albeit connected, microgrid and communication network topologies.