Objective. When listening to continuous speech, populations of neurons in the brain track different features of the signal. Neural tracking can be measured by relating the electroencephalography (EEG) and the speech signal. Recent studies have shown a significant contribution of linguistic features over acoustic neural tracking using linear models. However, linear models cannot model the nonlinear dynamics of the brain. To overcome this, we use a convolutional neural network (CNN) that relates EEG to linguistic features using phoneme or word onsets as a control and has the capacity to model non-linear relations. Approach. We integrate phoneme- and word-based linguistic features (phoneme surprisal, cohort entropy (CE), word surprisal (WS) and word frequency (WF)) in our nonlinear CNN model and investigate if they carry additional information on top of lexical features (phoneme and word onsets). We then compare the performance of our nonlinear CNN with that of a linear encoder and a linearized CNN. Main results. For the non-linear CNN, we found a significant contribution of CE over phoneme onsets and of WS and WF over word onsets. Moreover, the non-linear CNN outperformed the linear baselines. Significance. Measuring coding of linguistic features in the brain is important for auditory neuroscience research and applications that involve objectively measuring speech understanding. With linear models, this is measurable, but the effects are very small. The proposed non-linear CNN model yields larger differences between linguistic and lexical models and, therefore, could show effects that would otherwise be unmeasurable and may, in the future, lead to improved within-subject measures and shorter recordings.