PSR J1023+0038 is a rapidly-spinning neutron star with a low-mass-binary companion that switches between a radio pulsar and low-luminosity disk state. In 2013, it transitioned to its current disk state accompanied by brightening at all observed wavelengths. In this state, PSR J1023+0038 now shows optical and X-ray pulsations and abrupt X-ray luminosity switches between discrete low and high modes. Continuum radio emission, denoting an outflow, is also present and brightens during the X-ray low modes. Here, we present a simultaneous optical, ultraviolet (UV) and X-ray campaign comprising Kepler ($400-800$ nm), Hubble Space Telescope ($180-280$ nm), XMM-Newton ($0.3-10$ keV) and NuSTAR ($3 - 79$ keV). We demonstrate that low and high luminosity modes in the UV band are strictly simultaneous with the X-ray modes and change the UV brightness by a factor of $sim25$% on top of a much brighter persistent UV component. We find strong evidence for UV pulsations (pulse fraction of $0.82pm0.19$%) in the high-mode, with a similar waveform as the X-ray pulsations making it the first known UV millisecond pulsar. Lastly, we find that the optical mode changes occur synchronously with the UV/X-ray mode changes, but optical modes are inverted compared to the higher frequencies. There appear to be two broad-band emission components: one from radio to near-infrared/optical that is brighter when the second component from optical to hard X-rays is dimmer (and vice-versa). We suggest that these components trace switches between accretion into the neutron star magnetosphere (high-energy high-mode) versus ejection of material (low-energy high-mode). Lastly, we propose that optical/UV/X-ray pulsations can arise from a shocked accretion flow channeled by the neutron stars magnetic field.
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