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The role of pickup ions (PUIs) in the solar wind interaction with the local interstellar medium is investigated with 3D, multifluid simulations. The flow of the mixture of all charged particles is described by the ideal MHD equations, with the source terms responsible for charge exchange between ions and neutral atoms. The thermodynamically distinct populations of neutrals are governed by individual sets of gas dynamics Euler equations. PUIs are treated as a separate, comoving fluid. Because the anisotropic behavior of PUIs at the heliospheric termination shocks is not described by the standard conservation laws (a.k.a. the Rankine–Hugoniot relations), we derived boundary conditions for them, which are obtained from the dedicated kinetic simulations of collisionless shocks. It is demonstrated that this approach to treating PUIs makes the computation results more consistent with observational data. In particular, the PUI pressure in the inner heliosheath (IHS) becomes higher by ∼40%–50% in the new model, as compared with the solutions where no special boundary conditions are applied. Hotter PUIs eventually lead to charge-exchange-driven cooling of the IHS plasma, which reduces the IHS width by ∼15% (∼8–10 au) in the upwind direction, and even more in the other directions. The density of secondary neutral atoms born in the IHS decreases by ∼30%, while their temperature increases by ∼60%. Simulation results are validated with New Horizons data at distances between 11 and 47 au.