To meet the higher demands of the lightweight industry, composite materials are used for weight-bearing structures. Due to their superior properties, CFRP-Aluminium Stacks are especially attractive for many applications in the aerospace industry. Using rivets to connect these materials requires precise boreholes in large numbers, which are usually drilled. Because of the anisotropic material properties, high demands on the tool performance and process stability are set. Damages such as delamination, fibre pull-outs and inadequate surface properties are frequently observed at the drilled boreholes. To improve the monitoring status and failure detection, acoustic emission during drilling was analysed using the discrete wavelet transform method. By converting time signals into multiple independent time-frequency signals, temporary events during the monitoring of the cutting processes can be found. The studies show that certain combinations of wavelet families are particularly useful for describing correlations between acoustic emission and the delamination of the CFRP surface.