The aim of this study is to investigate the role of genetics and environment in susceptibility to breast cancer (frailty). An interdisciplinary approach was adopted, combining a correlated frailty-mixture model with genetic equations, allowing for decomposition of the frailty variance into genetic and environmental components. In addition, the possibility that a fraction of the population under study is 'immune' to the disease is evaluated, and changes in heritability estimates introducing a fraction of non-susceptible individuals are determined. The methodology is applied to breast cancer data from the Swedish Twin Registry, including information about all female monozygotic and dizygotic twin pairs born in Sweden between 1886 and 1967. The inferential problem is solved in a Bayesian framework and the numerical work is carried out using Markov chain Monte Carlo (MCMC) methods.