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Ground-based two-channel microwave radiometers (MWRs) have been used for over 15 years by the Atmospheric Radiation Measurement (ARM) program to provide observations of downwelling emitted radiance from which precipitable water vapor (PWV) and liquid water path (LWP) - two geophysical parameters critical for many areas of atmospheric research - are retrieved. An algorithm that incorporates output from two advanced retrieval techniques, namely, a physical-iterative approach and a computationally efficient statistical method, has been developed to retrieve these parameters. The forward model used in both methods is the monochromatic radiative transfer model MonoRTM. An important component of this MWR RETrieval (MWRRET) algorithm is the determination of small (< 1 K) offsets that are subtracted from the observed brightness temperatures before the retrievals are performed. Accounting for these offsets removes systematic biases from the observations and/or the model spectroscopy necessary for the retrieval, significantly reducing the systematic biases in the retrieved LWP. The MWRRET algorithm significantly provides more accurate retrievals than the original ARM statistical retrieval, which uses monthly retrieval coefficients. By combining the two retrieval methods with the application of brightness temperature offsets to reduce the spurious LWP bias in clear skies, the MWRRET algorithm significantly provides better retrievals of PWV and LWP from the ARM two-channel MWRs compared to the original ARM product.