We perform a global fit to ~5000 radial velocity and ~177000 magnitude measurements in 29 photometric bands covering 0.3{mu}m to 8.0{mu}m distributed among 287 Galactic, Large Magellanic Cloud, and Small Magellanic Cloud Cepheids with P>10 days. We assume that the Cepheid light curves and radial velocities are fully characterized by distance, reddening, and time-dependent radius and temperature variations. We construct phase curves of radius and temperature for periods between 10 and 100 days, which yield light-curve templates for all our photometric bands and can be easily generalized to any additional band. With only four to six parameters per Cepheid, depending on the existence of velocity data and the amount of freedom in the distance, the models have typical rms light and velocity curve residuals of 0.05mag and 3.5km/s. The model derives the mean Cepheid spectral energy distribution and its derivative with respect to temperature, which deviate from a blackbody in agreement with metal-line and molecular opacity effects. We determine a mean reddening law toward the Cepheids in our sample, which is not consistent with standard assumptions in either the optical or near-IR. Based on stellar atmosphere models, we predict the biases in distance, reddening, and temperature determinations due to the metallicity and quantify the metallicity signature expected for our fit residuals.