  We rigorously analyze the low-temperature properties of homogeneous
three-dimensional two-component Bose mixture with dipole-dipole interaction.
For such a system the effective hydrodynamic action that governs the behavior
of low-energy excitations is derived. The infrared structure of the exact
single-particle Green's functions is obtained in terms of macroscopic
parameters, namely the inverse compressibility and the superfluid density
matrices. Within one-loop approximation we calculate the anisotropic superfluid
and condensate densities and give the beyond mean-field stability condition for
the binary dipolar Bose gas. A brief variational derivation of the coupled
equations that describe macroscopic hydrodynamics of the system in the external
non-uniform potential at zero temperature is presented.
