We present improved synthesis models of the evolving spectrum of the UV/X-ray diffuse background, updating and extending our previous results. Five new main components are added to our radiative transfer code CUBA: (1) the sawtooth modulation of the background intensity from resonant line absorption in the Lyman series of cosmic hydrogen and helium; (2) the X-ray emission from the obscured and unobscured quasars that gives origin to the X-ray background; (3) a piecewise parameterization of the distribution in redshift and column density of intergalactic absorbers that fits recent measurements of the mean free path of 1 ryd photons; (4) an accurate treatment of the photoionization structure of absorbers, which enters in the calculation of the helium continuum opacity and recombination emissivity; and (5) the UV emission from star-forming galaxies at all redshifts. We provide tables of the predicted H i and He ii photoionization and photoheating rates for use, e.g., in cosmological hydrodynamics simulations of the Lyα forest and a new metallicity-dependent calibration to the UV luminosity density-star formation rate density relation. A "minimal cosmic reionization model" is also presented in which the galaxy UV emissivity traces recent determinations of the cosmic history of star formation, the luminosity-weighted escape fraction of hydrogen-ionizing radiation increases rapidly with look-back time, the clumping factor of the highredshift intergalactic medium evolves following the results of hydrodynamic simulations, and Population III stars and miniquasars make a negligible contribution to the metagalactic flux. The model provides a good fit to the hydrogenionization rates inferred from flux decrement and proximity effect measurements, predicts that cosmological H ii (He iii) regions overlap at redshift 6.7 (2.8), and yields an optical depth to Thomson scattering, τ es = 0.084 that is in agreement with Wilkinson Microwave Anisotropy Probe results. Our new background intensities and spectra are sensitive to a number of poorly determined input parameters and suffer from various degeneracies. Their predictive power should be constantly tested against new observations. We are therefore making our redshift-dependent UV/X emissivities and CUBA outputs freely available for public use at http://www.ucolick.org/∼pmadau/CUBA.