A treatment showing that the local interstellar medium (LISM) bow shock (BS) may exist and the heliosphere is tilted has recently been given by Ben-Jaffel et al.<2000> and used in an attempt to interpret combined Voyager UVS data and Hubble Space Telescope spectra of the Ly α sky background emission as plausible evidence for the existence of BS. However, the authors stressed the need for a more accurate description of the interface region in order to interpret the available data confidently. In this paper we use a more sophisticated Three-Dimensional Time-Dependent Magnetohydrodynamic with Neutral Particles (3DT MHD + N) model of the interaction between the solar wind and the interstellar medium with LISM neutral particles included. We report a parametric study of the effect of the LISM magnetic field strength and inclination angle in the presence of the neutral H atoms on the heliosphere and the heliospheric boundary. Ninety model cases that have been analyzed facilitate in building a diagnostic tool either to interpret archive data on the sky background radiation field or to stimulate new observations related to the interface, observations that may capture some of the fine structure revealed by the new model. Because the inclination angle and strength of the interstellar magnetic field induce unambiguous signatures in the heliospheric structure, our model calculations may serve as a lever to constrain the nature of the LISM from observational data.