This paper presents an algorithm that relies on a series of dense and deep neural networks for passive microwave retrieval of precipitation. The neural networks learn from coincidences of brightness temperatures from the Global Precipitation Measurement (GPM) Microwave Imager (GMI) with the active precipitating retrievals from the Dual-frequency Precipitation Radar (DPR) onboard GPM as well as those from the {CloudSat} Profiling Radar (CPR). The algorithm first detects the precipitation occurrence and phase and then estimates its rate, while conditioning the results to some key ancillary information including parameters related to cloud microphysical properties. The results indicate that we can reconstruct the DPR rainfall and CPR snowfall with a detection probability of more than 0.95 while the probability of a false alarm remains below 0.08 and 0.03, respectively. Conditioned to the occurrence of precipitation, the unbiased root mean squared error in estimation of rainfall (snowfall) rate using DPR (CPR) data is less than 0.8 (0.1) mm/hr over oceans and land. Beyond methodological developments, comparing the results with ERA5 reanalysis and official GPM products demonstrates that the uncertainty in global satellite snowfall retrievals continues to be large while there is a good agreement among rainfall products. Moreover, the results indicate that CPR active snowfall data can improve passive microwave estimates of global snowfall while the current CPR rainfall retrievals should only be used for detection and not estimation of rates.