In this paper register based family studies provide the motivation for linking a two-stage estimation procedure in copula models for multivariate failure time data with a composite likelihood approach. The asymptotic properties of the estimators in both parametric and semi-parametric models are derived, combining the approaches of Parner (2001) and Andersen (2003). The method is mainly studied when the families consist of groups of exchangeable members (e.g. siblings) or members at different levels (e.g. parents and children). The advantages of the proposed method are especially clear in this last case where very flexible modelling is possible. The suggested method is also studied in simulations and found to be efficient compared to maximum likelihood. Finally, the suggested method is applied to a family study of deep venous thromboembolism where it is seen that the association between ages at onset is larger for siblings than for parents or for parents and siblings.