Negative-index refraction is demonstrated in a lamellar composite with epsilon-negative (ENG) and mu-negative (MNG) materials stacked alteatively. Based on the effective medium approximation, simultaneously negative effective permittivity and permeability of such a lamellar composite are obtained theoretically and further proven by full-wave simulations. Consequently, the renowned left-handed metamaterial comprising split ring resonators and wires is interpreted as an analogy of such ENG-MNG layers. In addition, beyond the effective medium approximation, the propagating field squeezed near the ENG/MNG interface is demonstrated to be left-handed surface waves with backward phase velocity.