The communication networks obtained by using mobile phone datasets have drawn increasing attention in recent years. Studies have led to important advances in understanding the behavior of mobile users although they have just considered text message (short message service (SMS)), call data, and spatial proximity, separately. However, there is a growing awareness that human sociality is expressed simultaneously on multiple layers, each corresponding to a specific way an individual has to communicate. In fact, besides the common real life encounters, a mobile phone user has at least two further communication media to exploit, SMSs and voice calls. This is advocating a multidimensional approach if we are seeking a compound description of the human mobile social behavior. In this context, we perform the first study of the multiplex mobile network, gathered from the records of both call and text message activities, along with relevant geographical information, of millions of users of a large mobile phone operator over a period of 12 weeks. By computing a set of complex network metrics, at different scales, onto the three single layers given by calls, SMSs and spatial proximity, and their extensions onto a three-level network, we provide a comprehensive study of the global multi-layered network which arises from both the overall on-the-phone communications performed by mobile users and their spatial propinquity.