Non-intrusive load monitoring (NILM) is the task of determining the appliances individual contributions to the aggregate power consumption by using a set of electrical parameters measured at a single metering point. NILM allows to provide detailed consumption information to the users, that induces them to modify their habits towards a wiser use of the electrical energy. This paper proposes a NILM algorithm based on the joint use of active and reactive power in the Additive Factorial Hidden Markov Models framework. In particular, in the proposed approach, the appliance model is represented by a bivariate Hidden Markov Model whose emitted symbols are the joint active-reactive power signals. The disaggregation is performed by means of an alternative formulation of the Additive Factorial Approximate Maximum a Posteriori (AFAMAP) algorithm for dealing with the bivariate HMM models. The proposed solution has been compared to the original AFAMAP algorithm based on the active power only and to the seminal approach proposed by Hart (1992), based on finite state machine appliance models and which employs both the active and reactive power. Hart's algorithm has been improved for handling the occurrence of multiple solutions by means of a Maximum A Posteriori technique (MAP). The experiments have been conducted on the AMPds dataset in noised and denoised conditions and the performance evaluated by using the F-1-Measure and the normalized disaggregation metrics. In terms of F-1-Measure, the results showed that the proposed approach outperforms AFAMAP, Hart's algorithm, and Hart's with MAP respectively by + 14.9%, + 21.8%, and + 2.5% in the 6 appliances denoised case study. In the 6 appliances noised case study, the relative performance improvement is + 25.5%, + 51.1%, and + 6.7%.