The “cocktail party” problem—how a listener perceives speech in noisy environments—is typically studied using speech (multi-talker babble) or noise maskers. However, realistic cocktail party scenarios often include background music (e.g., coffee shops, concerts). Studies investigating music’s effects on concurrent speech perception have predominantly used highly controlled synthetic music or shaped noise, which do not reflect naturalistic listening environments. Behaviorally, familiar background music and songs with vocals/lyrics inhibit concurrent speech recognition. Here, we investigated the neural bases of these effects. While recording multichannel EEG, participants listened to an audiobook while popular songs (or silence) played in the background at a 0 dB signal-to-noise ratio. Songs were either familiar or unfamiliar to listeners and featured either vocals or isolated instrumentals from the original audio recordings. Comprehension questions probed task engagement. We used temporal response functions (TRFs) to isolate cortical tracking to the target speech envelope and analyzed neural responses around 100 ms (i.e., auditory N1 wave). We found that speech comprehension was, expectedly, impaired during background music compared to silence. Target speech tracking was further hindered by the presence of vocals. When masked by familiar music, response latencies to speech were less susceptible to informational masking, suggesting concurrent neural tracking of speech was easier during music known to the listener. These differential effects of music familiarity were further exacerbated in listeners with less musical ability. Our neuroimaging results and their dependence on listening skills are consistent with early attentional-gain mechanisms where familiar music is easier to tune out (listeners already know the song’s expectancies) and thus can allocate fewer attentional resources to the background music to better monitor concurrent speech material.