We present in this work a new reconstruction scheme, so-called MUSCL-THINC-BVD scheme, to solve the five-equation model for interfacial two phase flows. This scheme employs the traditional shock capturing MUSCL (Monotone Upstream-centered Schemes for Conservation Law) scheme as well as the interface sharpening THINC (Tangent of Hyperbola for INterface Capturing) scheme as two building-blocks of spatial reconstruction on the BVD (boundary variation diminishing) principle that minimizes the variations (jumps) of the reconstructed variables at cell boundaries, and thus effectively reduces the dissipation error in numerical solutions. The MUSCL-THINC-BVD scheme is implemented to the volume fraction and other state variables under the same finite volume framework, which realizes the consistency among volume fraction and other physical variables. Numerical results of benchmark tests show that the present method is able to capture the material interface as a well-defined sharp jump in volume fraction, and obtain numerical solutions of superior quality in comparison to other existing methods. The proposed scheme is a simple and effective method of practical significance for simulating compressible interfacial multiphase flows. •A novel paradigm of spatial reconstruction for compressible multi-phase flows with free interfaces.•Consistency among volume fraction and physical variables across moving material interfaces.•Well resolved moving interface free from numerical dissipation and smearing.•Algorithmic simplicity, computational efficiency and practical significance.•Superior numerical results for wide range benchmark tests to other existing methods.