  We discuss vacuum static, spherically symmetric asymptotically flat solutions
of the generalized hybrid metric-Palatini theory of gravity (generalized HMPG)
suggested by B\"ohmer and Tamanini, involving both a metric $g_{\mu\nu}$ and an
independent connection $\hat \Gamma_{\mu\nu}{}^\alpha$; the gravitational field
Lagrangian is an arbitrary function $f(R,P)$ of two Ricci scalars, $R$ obtained
from $g_{\mu\nu}$ and $P$ obtained from $\hat \Gamma_{\mu\nu}{}^\alpha$. The
theory admits a scalar-tensor representation with two scalars $\phi$ and $\xi$
and a potential $V(\phi,\xi)$ whose form depends on $f(R,P)$. Solutions are
obtained in the Einstein frame and transferred back to the original Jordan
frame for a proper interpretation. In the completely studied case $V \equiv 0$,
generic solutions contain naked singularities or describe traversable
wormholes, and only some special cases represent black holes with extremal
horizons. For $V(\phi,\xi) \ne 0$, some examples of analytical solutions are
obtained and shown to possess naked singularities. Even in the cases where the
Einstein-frame metric $g^E_{\mu\nu}$ is found analytically, the scalar field
equations need a numerical study, and if $g^E_{\mu\nu}$ contains a horizon, in
the Jordan frame it turns to a singularity due to the corresponding conformal
factor.
