This paper focuses on molecular communication (MC) systems using two types of signaling molecules which may participate in a reversible bimolecular reaction in the channel. The motivation for studying these MC systems is that they can realize the concept of constructive and destructive signal superposition, which leads to favorable properties such as inter-symbol interference (ISI) reduction and avoiding environmental contamination due to continuous release of signaling molecules into the channel. This work first presents a general formulation for binary modulation schemes that employ two types of signaling molecules and proposes several modulation schemes as special cases. Moreover, two types of receivers are considered: a receiver that is able to observe both types of signaling molecules (2TM), and a simpler receiver that can observe only one type of signaling molecules (1TM). For both of these receivers, the maximum likelihood (ML) detector for general binary modulation is derived under the assumption that the detector has perfect knowledge of the ISI-causing sequence. In addition, two suboptimal detectors of different complexity are proposed, namely an ML-based detector that employs an estimate of the ISI-causing sequence and a detector that neglects the effect of ISI. The proposed detectors, except for the detector that neglects ISI for the 2TM receiver, require knowledge of the channel response (CR) of the considered MC system. Moreover, the CR is needed for performance evaluation of all proposed detectors. However, deriving the CR of MC systems with reactive signaling molecules is challenging since the underlying partial differential equations that describe the reaction-diffusion mechanism are coupled and non-linear. Therefore, we develop an algorithm for efficient computation of the CR and validate its accuracy via particle-based simulation.