We present a new type of near-zero index (NZI) and epsilon near-zero (ENZ) metametarial with broad bandwidth characteristics. We propose an optimal geometry to manipulate the properties of the composite material and realize a metallic-dielectric NZI effective material operating at microwave frequencies with a broadband near-zero response. The effective material is composed by multiple layers of dissimilar metasurfaces of subwavelength dimensions. We demonstrate the broadband NZI metamaterial properties and study its anisotropy by realizing a radiating structure exhibiting broadband directive emission. An experimental demonstration validates the concept for an antenna in the microwave domain.