The two surfaces of a thin film with a thickness L described by the transverse Ising model are coupled to the inner next layer with a negative exchange interaction, so that the spin direction at the surfaces is opposite to that of the inner layers. The influences of exchange interactions, transverse fields and thickness on the longitudinal and transverse magnetizations of the thin film are investigated by the use of the standard mean-field theory. The longitudinal magnetization of a thin film is strongly affected by the ratios of the exchange interactions and the transverse fields between the surfaces and the bulk. In particular, some typical ferrimagnetic behaviours are found for the temperature dependence of longitudinal magnetization in the thin film, depending on these ratios and the transverse field in the bulk. The possibility of two compensation points is also found for the system with L = 10.