To understand the role of mammographic density on breast cancer risk, it is important to take into account body mass index (BMI). As with age, BMI is negatively confounded with mammographic density, and a previous US twin study found that the covariance structure of mammographic density depended on the extent to which pairs differ in BMI. Using a computerised thresholding technique, we measured mammographic dense area for 571 monozygous (MZ) and 380 dizygous (DZ) twin pairs aged 40-70 years from Australia and North America. After adjusting for age and BMI, we calculated estimates of variance, covariance, correlation and, under the assumptions of the classic twin model, additive genetic (A), common environment (C) and person-specific environmental (E) components of variance. Analyses were conducted both within and across categories of within-pair differences in BMI, under a bivariate normal model using the software FISHER. The variance, MZ and DZ correlations, and the differences between MZ and DZ correlations and covariances were not constant across absolute within-pair differences in BMI (for the DZ correlation, P = 0.04, all other P < 0.001). No model involving a combination of one or more of A, C and E gave an acceptable fit. The interpretation of these observations is not straightforward. They, and other data, challenge the assumptions of the classic twin model for mammographic density and suggest that an insightful test of those assumptions can be made by testing the stability of correlations, covariances and variance components across absolute within-pair differences in potential mediators.