  We present the publicly available model \textsc{reltrans} that calculates the
light-crossing delays and energy shifts experienced by X-ray photons originally
emitted close to the black hole when they reflect from the accretion disk and
are scattered into our line-of-sight, accounting for all general relativistic
effects. Our model is fast and flexible enough to be simultaneously fit to the
observed energy-dependent cross-spectrum for a large range of Fourier
frequencies, as well as to the time-averaged spectrum. This not only enables
better geometric constraints than only modelling the relativistically broadened
reflection features in the time-averaged spectrum, but additionally enables
constraints on the mass of supermassive black holes in active galactic nuclei
and stellar-mass black holes in X-ray binaries. We include a self-consistently
calculated radial profile of the disk ionization parameter and properly account
for the effect that the telescope response has on the predicted time lags. We
find that a number of previous spectral analyses have measured artificially low
source heights due to not accounting for the former effect and that timing
analyses have been affected by the latter. In particular, the magnitude of the
soft lags in active galactic nuclei may have been under-estimated, and the
magnitude of lags attributed to thermal reverberation in X-ray binaries may
have been over-estimated. We fit \textsc{reltrans} to the lag-energy spectrum
of the Seyfert galaxy Mrk 335, resulting in a best fitting black hole mass that
is smaller than previous optical reverberation measurements ($\sim 7$ million
compared with $\sim14-26$ million $M_\odot$).
