Inspired by the hierarchical hidden Markov models (HHMM), we present the hierarchical conditional random field (HCRF), a generalisation of embedded undirected Markov chains to model complex hierarchical, nested Markov processes. It is parameterised in a discriminative framework and has polynomial time algorithms for learning and inference. Importantly, we consider partially-supervised learning and propose algorithms for generalised partially-supervised learning and constrained inference. We demonstrate the HCRF in two applications: (i) recognising human activities of daily living (ADLs) from indoor surveillance cameras, and (ii) noun-phrase chunking. We show that the HCRF is capable of learning rich hierarchical models with reasonable accuracy in both fully and partially observed data cases.