Recently, microwave communication networks have been shown to be valuable tools for rainfall monitoring, based on the well-known Power-Law which relates rain-rate to attenuation in microwave frequencies. However, once precipitation other than pure rain exists (e.g., snow), the Power-Law relation is no longer accurate. In this paper we propose a model which relates the induced attenuation to rain, snow, and sleet. Based on this model we propose estimating the total accumulated precipitation, regardless of the precipitation type, using measurements from multiple microwave links. Our technique takes advantage of the commercial communication networks, need for redundancy, which dictates the use of multiple microwave links at the same area. We show that by using measurements from at least three microwave links better estimation of the total accumulated precipitation fall can be provided, when rain, snow, sleet, or a mixture of them coexists. To demonstrate the proposed approach, it has been applied on actual microwave links attenuation measurements, which were provided by a cellular carrier. The estimation results were compared with Rain-Gauges and disdrometer measurements and show very good agreement and improved accuracy.