Face morphing and related morphing attacks have emerged as a serious security threat for automatic face recognition systems and a challenging research field. Therefore, the availability of effective and reliable morphing attack detectors is strongly needed. In this paper, we proposed a framework based on a double Siamese architecture to tackle the morphing attack detection task in the differential scenario, in which two images, a trusted live acquired image and a probe image (morphed or bona fide) are given as the input for the system. In particular, the presented framework aimed to merge the information computed by two different modules to predict the final score. The first one was designed to extract information about the identity of the input faces, while the second module was focused on the detection of artifacts related to the morphing process. Experimental results were obtained through several and rigorous cross-dataset tests, exploiting three well-known datasets, namely PMDB, MorphDB, and AMSL, containing automatic and manually refined facial morphed images, showing that the proposed framework was able to achieve satisfying results.