  Mutually misaligned circumbinary planets may form in a warped or broken gas
disc or from later planet-planet interactions. With numerical simulations and
analytic estimates we explore the dynamics of two circumbinary planets with a
large mutual inclination. A coplanar inner planet causes prograde apsidal
precession of the binary and the stationary inclination for the outer planet is
higher for larger outer planet orbital radius. In this case a coplanar outer
planet always remains coplanar. On the other hand, a polar inner planet causes
retrograde apsidal precession of the binary orbit and the stationary
inclination is smaller for larger outer planet orbital radius. For a range of
outer planet semi-major axes, an initially coplanar orbit is librating meaning
that the outer planet undergoes large tilt oscillations. Circumbinary planets
that are highly inclined to the binary are difficult to detect -- it is
unlikely for a planet to have an inclination below the transit detection limit
in the presence of a polar inner planet. These results suggest that there could
be a population of circumbinary planets that are undergoing large tilt
oscillations.
