There is ongoing debate within the field of bilingual education concerning the extent to which instructional languages should be separated. However, neither side has sufficiently addressed how language practices and policies shape the ideological space of the classroom, and the concomitant implications for student learning and sense-making around bilingualism. This article interrogates how programmatic binaries within a second-grade two-way bilingual education (TWBE) classroom emerge in and through classroom discourse in ways that (re)enforce the ideological construction of "two" languages and "two" groups of learners. Drawing upon microethnographic discourse analysis and positioning theory, I conduct a close analysis of one illustrative classroom language event, revealing how students are discursively positioned as either Spanish-speakers/Latinos or English-speakers/Anglos. Through this analysis, I demonstrate the complexity of identity positioning in TWBE, revealing how the reification of binaries affirms Latinx student identities while simultaneously reinforcing monoglossic framings of bilingualism and overly simplistic understandings of students' linguistic identities. Findings point to the need to critically reimagine how two-ness is constructed and negotiated in TWBE and to better account for the interrelation among classroom practices, language ideologies, and student identities.