In HELIOS, a two-dimensional program for fuel assembly calculations, the geometric system can be partitioned into heterogeneous space elements. The transport of neutrons and gammas is treated by the CCCP method: current coupling (CC) of the space elements, which are internally treated by collision probabilities (CPs). The region-to-region, region-to-surface, surface-to-region, and surface-to-surface probabilities are evaluated. They are numerically integrated according to Carlvik’s method. It is illustrated that elaborate ray tracing and careful normalization prevent the instabilities that the CPs would otherwise suffer. The angular dependence of the interface currents introduces angular dependence into the last three of these probabilities. A reciprocity relation between region-to-surface and surface-to-region probabilities is derived for the individual angular sectors at the surfaces. Also, a new integral function is introduced, the partial Bickley function. An efficient evaluation method for both normal and partial Bickley functions is presented that reduces the computational time for the CPs by ∼20%.