A statistical methodology to combine measurements from space-borne microwave radar and radiometers is proposed. The approach is fairly general, even though the combination technique is here tailored for the two instruments onboard the Tropical Rainfall Measuring Mission (TRMM) satellite specifically devoted to rainfall measurements, that is, the Precipitation Radar (PR) and the TRMM Microwave Imager (TMI). Two combined retrieval algorithms are proposed, both derived from the previously developed Bayesian algorithm for microwave-based precipitation retrieval from passive sensors (BAMPR-P), which is based on a Bayesian inversion method and is trained by a modeled cloud radiation database. The first combined technique, called BAMPR-C (BAMPR combined), operates in the narrower common swath aiming at exploiting the simultaneous measurements of PR and TMI instruments. Within BAMPR-C the hydrometeor profiles, retrieved from TMI, are used as a constraint for the PR-based inversion: this two step cascade allows us to overcome the difficulty to take into account the different scan geometries of TMI and PR. The second combined technique is called BAMPR-B (BAMPR broadening) and aims at improving the TMI-only retrieval outside the common swath. In this approach, first optimal retrieved profiles are generated by reversing the order of the previous two steps of BAMPR-C cascade within the common swath. Then the resulting profile data set and the corresponding TMI brightness temperatures are used to define the cloud radiation database to be employed outside the common swath for the TMI-only retrieval, achieving the so-called radar swath synthetic broadening. Numerical internal tests, using simulated data, are illustrated to quantify the features of the proposed synergetic algorithms. Finally, an application to measured TRMM data for a selected case study (hurricane Bonnie on August 1998) is shown and discussed.