We propose a novel hierarchical approach for the classification of airborne 3D lidar points. Spatial and semantic context is incorporated via a two-layer Conditional Random Field (CRF). The first layer operates on a point level and utilises higher order cliques. Segments are generated from the labelling obtained in this way. They are the entities of the second layer, which incorporates larger scale context. The classification result of the segments is introduced as an energy term for the next iteration of the point-based layer. This framework iterates and mutually propagates context to improve the classification results. Potentially wrong decisions can be revised at later stages. The output is a labelled point cloud as well as segments roughly corresponding to object instances. Moreover, we present two new contextual features for the segment classification: the distance and the orientation of a segment with respect to the closest road. It is shown that the classification benefits from these features. In our experiments the hierarchical framework improve the overall accuracies by 2.3% on a point-based level and by 3.0% on a segment-based level, respectively, compared to a purely point-based classification.