Language rhythm determines young infants' language discrimination abilities. However, it is unclear whether young bilingual infants exposed to rhythmically similar languages develop sensitivities to cross-linguistic rhythm cues to discriminate their dual language input. To address this question, 3.5-month-old monolingual Basque, monolingual Spanish and bilingual Basque-Spanish infants' language discrimination abilities (across low-pass filtered speech samples of Basque and Spanish) have been tested using the visual habituation procedure. Although falling within the same rhythmic class, Basque and Spanish exhibit significant differences in their distributions of vocalic intervals (within-rhythmic class variation). All infant groups in our study successfully discriminated between the languages, although each group exhibited a different pattern. Monolingual Spanish infants succeeded only when they heard Basque during habituation, suggesting that they were influenced by native language recognition. The bilingual and the Basque monolingual infants showed no such asymmetries and succeeded irrespective of the language of habituation. Additionally, bilingual infants exhibited longer looking times in the test phase as compared with monolinguals, reflecting that bilingual infants attend to their native languages differently than monolinguals. Overall, results suggest that bilingual infants are sensitive to within-rhythm acoustic regularities of their native language(s) facilitating language discrimination and hence supporting early bilingual acquisition.