This study investigates the internal representations of verb-particle combinations, called multi-word verbs, within transformer-based large language models (LLMs), specifically examining how these models capture lexical and syntactic properties at different neural network layers. Using the BERT architecture, we analyze the representations of its layers for two different verb-particle constructions: phrasal verbs like 'give up' and prepositional verbs like 'look at'. Our methodology includes training probing classifiers on the internal representations to classify these categories at both word and sentence levels. The results indicate that the model's middle layers achieve the highest classification accuracies. To further analyze the nature of these distinctions, we conduct a data separability test using the Generalized Discrimination Value (GDV). While GDV results show weak linear separability between the two verb types, probing classifiers still achieve high accuracy, suggesting that representations of these linguistic categories may be non-linearly separable. This aligns with previous research indicating that linguistic distinctions in neural networks are not always encoded in a linearly separable manner. These findings computationally support usage-based claims on the representation of verb-particle constructions and highlight the complex interaction between neural network architectures and linguistic structures.