Here, we used event-related potentials to test the predictions of two prominent accounts of code-switching in bilinguals: The Matrix Language Framework (MLF; Myers-Scotton, 1993) and an application of the Minimalist Program (MP; Cantone & MacSwan, 2009). We focused on the relative order of the noun with respect to the adjective in mixed Welsh-English nominal constructions given the clear contrast between pre- and post-nominal adjective position between Welsh and English. MP would predict that the language of the adjective should determine felicitous word order (i.e., English adjectives should appear pre-nominally and Welsh adjectives post-nominally). In contrast, MLF contends that it is the language of the finite verb inflection rather than that of a particular word that governs felicitous word order. To assess the predictions of the two models, we constructed sentences featuring a code-switch between the adjective and the noun, that complied with either English or Welsh word-order. Highly proficient Welsh-English bilinguals made semantic acceptability judgements upon reading the last word of sentences which could violate MP assumptions, MLF assumptions, both assumptions, or neither. Behaviourally, MP violations had no significant effect, whereas MLF violations induced an average drop of 11% in acceptability judgements. Neurophysiologically, MP violations elicited a significant Left Anterior Negativity (LAN) modulation, whereas MLF violations modulated both P600 and LAN mean amplitudes. In addition, there was a significant interaction between MP and MLF status in the P600 range: When MP was violated, MLF status did not matter, and when MP criteria were met, MLF violations resulted in a P600 modulation. This interaction possibly reflects a general preference for noun over adjective insertions, and may provide support for MLF over MP at a global sentence processing level. Model predictions also manifested differently in each of the matrix languages: When the matrix language was Welsh, MP and MLF violations elicited greater P600 mean amplitudes than MP and MLF adherences, however this pattern was not observed when the matrix language was English. We discuss methodological considerations relating to the neuroscientific study of code-switching, and the extent to which our results shed light on adjective-noun code-switching beyond findings from production and experimental-behavioural studies.