  The majority of binary stars do not eclipse. Current searches for transiting
circumbinary planets concentrate on eclipsing binaries, and are therefore
restricted to a small fraction of potential hosts. We investigate the concept
of finding planets transiting non-eclipsing binaries, whose geometry would
require mutually inclined planes. Using an N-body code we explore how the
number and sequence of transits vary as functions of observing time and orbital
parameters. The concept is then generalised thanks to a suite of simulated
circumbinary systems. Binaries are constructed from RV surveys of the solar
neighbourhood. They are then populated with orbiting gas giants, drawn from a
range of distributions. The binary population is shown to be compatible with
the Kepler eclipsing binary catalogue, indicating that the properties of
binaries may be as universal as the initial mass function. These synthetic
systems produce transiting circumbinary planets occurring on both eclipsing and
non-eclipsing binaries. Simulated planets transiting eclipsing binaries are
compared with published Kepler detections. We obtain 1) that planets transiting
non-eclipsing binaries probably exist in the Kepler data, 2) that observational
biases alone cannot account for the observed over-density of circumbinary
planets near the stability limit, implying a physical pile-up, and 3) that the
distributions of gas giants orbiting single and binary stars are likely
different. Estimating the frequency of circumbinary planets is degenerate with
the spread in mutual inclination. Only a minimum occurrence rate can be
produced, which we find to be compatible with 9%. Searching for inclined
circumbinary planets may significantly increase the population of known objects
and will test our conclusions. Their existence, or absence, will reveal the
true occurrence rate and help develop circumbinary planet formation theories.
