Segmentation and (segment) labeling are generally treated separately in lexical semantics, raising issues due to their close inter-dependence and necessitating joint annotation. We therefore investigate the lexical semantic recognition task of multiword expression segmentation and supersense disambiguation, unifying several previously-disparate styles of lexical semantic annotation. We evaluate a neural CRF model along all annotation axes available in version 4.3 of the STREUSLE corpus: lexical unit segmentation (multiword expressions), word-level syntactic tags, and supersense classes for noun, verb, and preposition/possessive units. As the label set generalizes that of previous tasks (DiMSUM, PARSEME), we additionally evaluate how well the model generalizes to those test sets, with encouraging results. By establishing baseline models and evaluation metrics, we pave the way for comprehensive and accurate modeling of lexical semantics.