The Sun is moving through a warm ( \sim 6500 K ) and partly ionized local interstellar cloud ( LIC ) with a velocity of \sim 26 km/s . Recent measurements of the ionization of the LIC ( Wolff et al. , 1999 ) suggest that interstellar helium in the vicinity of the Sun is 30-40 % ionized , while interstellar hydrogen is less ionized . Consequently , interstellar helium ions contribute up to 50 % of the total dynamic pressure of the ionized interstellar component . Up to now interstellar helium ions have been ignored in existing models of the heliospheric interface . In this paper we present results of a new model of the solar wind interaction with the interstellar medium , which takes into account interstellar helium ions . Using results of this model we find that the heliopause , termination and bow shocks are closer to the Sun when compared to the model results that ignore He ions . The influence of interstellar helium ions is partially compensated by solar wind alpha particles , which are taken into account in our new model as well . Finally , we apply our new model to place constraints on the plausible location of the termination shock .