  We investigate effects of dipole-dipole (DD) interactions on
immiscibility-miscibility transitions (IMTs) in two-component Bose-Einstein
condensates (BECs) trapped in the harmonic-oscillator (HO) potential, with the
components linearly coupled by a resonant electromagnetic field (accordingly,
the components represent two different spin states of the same atom). The
problem is studied by means of direct numerical simulations. Different mutual
orientations of the dipolar moments in the two components are considered. It is
shown that, in the binary BEC formed by dipoles with the same orientation and
equal magnitudes, the IMT cannot be induced by the DD interaction alone, being
possible only in the presence of the linear coupling between the components,
while the miscibility threshold is affected by the DD interactions. However, in
the binary condensate with the two dipolar components polarized in opposite
directions, the IMT can be induced \emph{without} any linear coupling. Further,
we demonstrate that those miscible and immiscible localized states, formed in
the presence of the DD interactions, which are unstable evolve into robust
breathers, which tend to keep the original miscibility or immiscibility,
respectively. An exception is the case of a very strong DD attraction, when
narrow stationary modes are destroyed by the instability. The binary BEC
composed of co-polarized dipoles with different magnitudes are briefly
considered too.
