Energy storage systems are becoming a key component in smart grids with increasing renewable penetration. Storage technologies feature diverse capacity, charging, and response specifications. Investment and degradation costs may require charging batteries at multiple timescales, potentially matching the control periods at which grids are dispatched. To this end, a microgrid equipped with slow- and fast-responding batteries is considered here. Energy management decisions are taken at two stages. Slow-responding batteries are dispatched at an hourly resolution with decisions remaining invariant over multiple fast control slots. Building on Lyapunov optimization, slow- and fast-responding batteries are charged based on real-time and data-dependent with quantifiable suboptimality bounds. Numerical tests using real data demonstrate the advantage of operating heterogeneous batteries.