We demonstrate a field-portable upright and inverted microscope that can image specimens in both reflection and transmission modes. This compact and cost-effective dual-mode microscope weighs only ∼135 grams (<4.8 ounces) and utilizes a simple light emitting diode (LED) to illuminate the sample of interest using a beam-splitter cube that is positioned above the object plane. This LED illumination is then partially reflected from the sample to be collected by two lenses, creating a reflection image of the specimen onto an opto-electronic sensor-array that is positioned above the beam-splitter cube. In addition to this, the illumination beam is also partially transmitted through the same specimen, which then casts lensfree in-line holograms of the same objects onto a second opto-electronic sensor-array that is positioned underneath the beam-splitter cube. By rapid digital reconstruction of the acquired lensfree holograms, transmission images (both phase and amplitude) of the same specimen are also created. We tested the performance of this field-portable microscope by imaging various micro-particles, blood smears as well as a histopathology slide corresponding to skin tissue. Being compact, light-weight and cost-effective, this combined reflection and transmission microscope might especially be useful for telemedicine applications in resource limited settings.