Owing to the omnidirectional perfect transmission and omnidirectional zero phase accumulation properties, S-type optical nihility media (ONM) have been utilized to design hyperlenses, optical waveguides, field concentrators and field rotators. Under the multiple interference mechanism, for conventional all-dielectric one-dimensional photonic crystals (1DPCs), all the transmittance peaks within the passband will shift towards short wavelengths (blueshift) with the increase in incident angle. Therefore, effective ONM cannot be realized in all-dielectric 1DPCs because the perfect transmission and zero phase accumulation conditions at the wavelength of the transmittance peak can only be satisfied at a specific incident angle. However, in a 1DPC composed of alternating dielectric and hyperbolic metamaterial (HMM) layers, one can realize a stopband of which one band edge is redshifted. At the same time, a transmittance peak in the passband is blueshifted. Therefore, between the redshift band edge and the blueshift transmittance peak, one can obtain an angle-independent transmittance peak. The HMM layer is mimicked by a dielectric/doped semiconductor multilayer. At the wavelength of the angle-independent transmittance peak, perfect transmission and zero phase accumulation conditions can be satisfied at any incident angle. Our work provides a route, under the current experimental conditions, to realize an effective S-type ONM by a simple one-dimensional structure in the near-infrared range.