Microwave radar and microwave-induced thermoacoustics, recently proposed as promising breast cancer detection techniques, each have shortcomings that reduce detection performance. Making the assumption that the measurement noises experienced when applying these two techniques are independent, we propose a methodology to process the input signals jointly based on a hypothesis testing framework. We present two test statistics and derive their distributions to set the thresholds. The methodology is evaluated on numerically simulated signals acquired from 2-D numerical breast models using finite-difference time-domain method. Our results show that the proposed dual-modality approach can give a significant improvement in detection performance.