We present an automatic non-invasive way of detecting cough events based on both accelerometer and audio signals. The acceleration signals are captured by a smartphone firmly attached to the patient’s bed, using its integrated accelerometer. The audio signals are captured simultaneously by the same smartphone using an external microphone. We have compiled a manually-annotated dataset containing such simultaneously-captured acceleration and audio signals for approximately 6000 cough and 68000 non-cough events from 14 adult male patients. Logistic regression (LR), support vector machine (SVM) and multilayer perceptron (MLP) classifiers provide a baseline and are compared with three deep architectures, convolutional neural network (CNN), long short-term memory (LSTM) network, and residual-based architecture (Resnet50) using a leave-one-out cross-validation scheme. We find that it is possible to use either acceleration or audio signals to distinguish between coughing and other activities including sneezing, throat-clearing, and movement on the bed with high accuracy. However, in all cases, the deep neural networks outperform the shallow classifiers by a clear margin and the Resnet50 offers the best performance, achieving an area under the ROC curve (AUC) exceeding 0.98 and 0.99 for acceleration and audio signals respectively. While audio-based classification consistently offers better performance than acceleration-based classification, we observe that the difference is very small for the best systems. Since the acceleration signal requires less processing power, and since the need to record audio is sidestepped and thus privacy is inherently secured, and since the recording device is attached to the bed and not worn, an accelerometer-based highly accurate non-invasive cough detector may represent a more convenient and readily accepted method in long-term cough monitoring.