We report an optical/UV jet and counterjet in M84, previously unreported in archival HST imaging. With archival VLA, ALMA, and Chandra imaging, we examine the first well-sampled spectral energy distribution of the inner jet of M84, where we find that multiple co-spatial spectral components are required. In particular, the ALMA data reveal that the radio spectrum of all four knots in the jet turns over at approximately 100 GHz, which requires a second component for the bright optical/UV emission. Further, the optical/UV has a soft spectrum and is inconsistent with the relatively flat X-ray spectrum, which indicates a third component at higher energies. Using archival VLA imaging, we have measured the proper motion of the innermost knots at 0.9+/-0.6 and 1.1+/-0.4 c, which when combined with the low jet-to-counterjet flux ratio yields an orientation angle for the system of 74 (+9,-18) degrees. In the radio, we find high fractional polarization of the inner jet of up to 30% while in the optical no polarization is detected (< 8%). We investigate different scenarios for explaining the particular multi-component SED of the knots. Inverse Compton models are ruled out due to the extreme departure from equipartition and the unrealistically high total jet power required. The multi-component SED can be naturally explained within a leptohadronic scenario, but at the cost of very high power in relativistic protons. A two-component synchrotron model remains a viable explanation, but more theoretical work is needed to explain the origin and properties of the electron populations.