As the coupling between transmission systems and distribution systems is significantly enhanced, transmission-distribution coordinated optimisation becomes more and more necessary. Considering that the objectives of the transmission system operator (TSO) and the distribution system operator (DSO) are usually significantly different in the type and dimension, a synthesised-objective collaborative model is proposed in this study, by normalising different objectives, introducing a weight factor to reflect the importance degree difference of multiple objectives and constructing a common objective. Then, a modified heterogeneous decomposition (M-HGD) algorithm is proposed to solve the model. In the M-HGD, two modifications on the update of iterative variables and the stop criteria are proposed, which effectively relieves the fluctuation of the iterative variables and restrains the tail effect of the convergence curve. The proposed model and algorithm can avoid privacy issues between the TSO and the DSO, achieve Pareto optimality solutions, and have powerful flexibility. Numerical experiments validate the effectiveness of the proposed model and demonstrate that the M-HGD has high accuracy and has better convergence and efficiency than traditional distributed optimisation methods.