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The soft X-ray pulsar RX J1856.5-3754 is the brightest member of a small class of thermally-emitting, radio-silent, isolated neutron stars. Its X-ray spectrum is almost indistinguishable from a blackbody with $kT^\infty\approx 60$ eV, but evidence of harder emission above $\sim 1$ keV has been recently found. We report on a spectral and timing analysis of RX J1856.5-3754 based on the large amount of data collected by XMM-Newton in 2002--2022, complemented by a dense monitoring campaign carried out by NICER in 2019. Through a phase-coherent timing analysis we obtained an improved value of the spin-down rate $\dotν=-6.042(4)\times10^{-16}$ Hz s$^{-1}$, reducing by more than one order magnitude the uncertainty of the previous measurement, and yielding a characteristic spin-down field of $1.47\times10^{13}$ G. We also detect two spectral components above $\sim1$ keV: a blackbody-like one with $kT^\infty=138\pm13$ eV and emitting radius $31_{-16}^{+8}$ m, and a power law with photon index $Γ=1.4_{-0.4}^{+0.5}$. The power-law 2--8\,keV flux, $(2.5_{-0.6}^{+0.7})\times10{-15}$ erg cm$^{-2}$ s$^{-1}$, corresponds to an efficiency of $10^{-3}$, in line with that seen in other pulsars. We also reveal a small difference between the $0.1$--$0.3$ keV and $0.3$--$1.2$ keV pulse profiles, as well as some evidence for a modulation above $1.2$ keV. These results show that, notwithstanding its simple spectrum, \eighteen still has a non-trivial thermal surface distribution and features non-thermal emission as seen in other pulsars with higher spin-down power.