Sparsity has been one of the major drives in signal processing in the last decade. Structured sparsity has also lately emerged as a way to enrich signal priors towards more meaningful and accurate representations. In this paper we propose a new structured sparsity signal model that allows for the decomposition of signals into structured molecules. We define the molecules to be linear combinations of atoms in a dictionary and we create a decomposition scheme that allows for their identification in noisy signals while being robust to small errors in the internal molecule structure. We show the effectiveness of our scheme for recovering and identifying corrupted or occluded signals on both synthetic and real data.