We use NEOWISE data from the four-band and three-band cryogenic phases of the Wide-field Infrared Survey Explorer mission to constrain size distributions of the comet populations and debias measurements of the short- and long-period comet (LPC) populations. We find that the fit to the debiased LPC population yields a cumulative size-frequency distribution (SFD) power-law slope ({beta}) of -1.0+/-0.1, while the debiased Jupiter-family comet (JFC) SFD has a steeper slope with {beta}=-2.3+/-0.2. The JFCs in our debiased sample yielded a mean nucleus size of 1.3km in diameter, while the LPCs' mean size is roughly twice as large, 2.1km, yielding mean size ratios (<D_LPC_>/<D_JFC_>) that differ by a factor of 1.6. Over the course of the 8 months of the survey, our results indicate that the number of LPCs passing within 1.5 au are a factor of several higher than previous estimates, while JFCs are within the previous range of estimates of a few thousand down to sizes near 1.3km in diameter. Finally, we also observe evidence for structure in the orbital distribution of LPCs, with an overdensity of comets clustered near 110{deg} inclination and perihelion near 2.9 au that is not attributable to observational bias.