This paper introduces a convolutional sparse model for anomaly detection in mixed continuous and discrete data. This model, referred to as C-ADDICT, builds upon the experiences of our previous ADDICT algorithm. It can handle discrete and continuous data jointly, is intrinsically shift-invariant, and crucially, it encodes each input signal (either continuous or discrete) from a joint activation and uniform combinations of filters, allowing the correlation across the input signals to be captured. The performance of C-ADDICT, is evaluated on a representative dataset composed of real spacecraft telemetries with an available ground-truth, providing promising results.