<p>Bivariate interval-censored failure time data occur in many areas such as biomedical and epidemiological research and their regression analysis has been discussed by many authors. However, most of the existing methods have some limitations on either data structures or the assumed models. In this paper, we propose a sieve maximum likelihood estimation approach for general interval-censored data under a class of flexible copula-based semiparametric partly linear transformation models. The approach allows for potential nonlinear effects and makes use of Bernstein polynomials. The resulting estimators of regression parameters are shown to be consistent and asymptotically efficient and normal. A simulation study is conducted to assess the finite-sample performance of the proposed approach and suggests that it works well in practice. Also we apply it to a set of real data arising from dental research.</p>