In the paper receiver structures which minimise the bit error probability for coherent detection of multi-h binary continuous phase modulation (CPM) signals for arbitrary number of observation intervals are examined by means of the traditional union bound at high SNR and by using the concept of the average matched filter (AMF) at low SNR. Multi-h schemes are found by upper-bound minimisation as a function of observation intervals and received SNR. Explicit expressions for the performance of the AMF receiver are derived for three important subclasses of binary multi-h CPM. Optimum and suboptimum receiver structures are examined. Several numerical examples are given, and a comparison of our results with the available results on binary CPM is provided.