The rapid spread of media content synthesis technology and the potentially damaging impact of audio and video deepfakes on people's lives have raised the need to implement systems able to detect these forgeries automatically. In this work we present a novel approach for synthetic speech detection, exploiting the combination of two high-level semantic properties of the human voice. On one side, we focus on speaker identity cues and represent them as speaker embeddings extracted using a state-of-the-art method for the automatic speaker verification task. On the other side, voice prosody, intended as variations in rhythm, pitch or accent in speech, is extracted through a specialized encoder. We show that the combination of these two embeddings fed to a supervised binary classifier allows the detection of deepfake speech generated with both Text-to-Speech and Voice Conversion techniques. Our results show improvements over the considered baselines, good generalization properties over multiple datasets and robustness to audio compression.