We present three new eclipsing white-dwarf/M-dwarf binary systems discovered during a search for transiting planets around M-dwarfs. Unlike most known eclipsing systems of this type, the optical and infrared emission is dominated by the M-dwarf components, and the systems have optical colors and discovery light curves consistent with being Jupiter-radius transiting planets around early M-dwarfs. We detail the PTF/M-dwarf transiting planet survey, part of the Palomar Transient Factory (PTF). We present a graphics processing unit (GPU)-based box- least-squares search for transits that runs approximately 8 × faster than similar algorithms implemented on general purpose systems. For the discovered systems, we decompose low-resolution spectra of the systems into white-dwarf and M-dwarf components, and use radial velocity measurements and cooling models to estimate masses and radii for the white dwarfs. The systems are compact, with periods between 0.35 and 0.45 days and semimajor axes of approximately 2 R $_☉$ (0.01 AU). The M-dwarfs have masses of approximately 0.35 M $_☉$, and the white dwarfs have hydrogen-rich atmospheres with temperatures of around 8000 K and have masses of approximately 0.5 M $_☉$. We use the Robo-AO laser guide star adaptive optics system to tentatively identify one of the objects as a triple system. We also use high-cadence photometry to put an upper limit on the white-dwarf radius of 0.025 R $_☉$ (95% confidence) in one of the systems. Accounting for our detection efficiency and geometric factors, we estimate that 0.08%̂+0.10%_-0.05% (90% confidence) of M-dwarfs are in these short-period, post-common-envelope white- dwarf/M-dwarf binaries where the optical light is dominated by the M-dwarf. The lack of detections at shorter periods, despite near-100% detection efficiency for such systems, suggests that binaries including these relatively low-temperature white dwarfs are preferentially found at relatively large orbital radii. Similar eclipsing binary systems can have arbitrarily small eclipse depths in red bands and generate plausible small-planet- transit light curves. As such, these systems are a source of false positives for M-dwarf transiting planet searches. We present several ways to rapidly distinguish these binaries from transiting planet systems.