  Let $ G $ be a connected, simply connected semisimple algebraic group over
the complex number field, and let $ K $ be the fixed point subgroup of an
involutive automorphism of $ G $ so that $ (G, K) $ is a symmetric pair.
  We take parabolic subgroups $ P $ of $ G $ and $ Q $ of $ K $ respectively
and consider the product of partial flag varieties $ G/P $ and $ K/Q $ with
diagonal $ K $-action, which we call a \emph{double flag variety for symmetric
pair}. It is said to be \emph{of finite type} if there are only finitely many $
K $-orbits on it.
  In this paper, we give a parametrization of $ K $-orbits on $ G/P \times K/Q
$ in terms of quotient spaces of unipotent groups without assuming the
finiteness of orbits. If one of $ P \subset G $ or $ Q \subset K $ is a Borel
subgroup, the finiteness of orbits is closely related to spherical actions. In
such cases, we give a complete classification of double flag varieties of
finite type, namely, we obtain classifications of $ K $-spherical flag
varieties $ G/P $ and $ G $-spherical homogeneous spaces $ G/Q $.
