Most researchers have studied students' academic self-concept within native language and mathematics, indicating the multidimensional nature of academic self-concept. However, there is a shortage of studies that examined the twofold multidimensional structure of verbal self-concept within the internal/external frame of reference (I/E) model of two foreign languages. This study aims to examine affective and cognitive components of English and Russian self-concepts for defining the separation or conflation of these components within the I/E model and evaluate cognitive and affective components across gender. A total of 540 eighth-grade Azeri students participated in this study. Confirmatory factor analysis indicated self-concept structure as twofold multidimensional, distinguishing affective and cognitive components as two different constructs. Study of the I/E model of two language self-concepts showed that Russian achievement correlated with Russian cognitive self-concept and English cognitive self-concept related to English achievement. One general verbal self-concept for different languages may not adequately represent multilingual learners and can produce misleading interpretations. The relationship between the two dimensions of self-concept in two target languages was invariant. The results of this study should encourage researchers to examine subject-specific self-concepts that conceptualize cognitive and affective dimensions of the self-concept and their relationships with achievement.