The critical behavior of a spin-1/2 Ising thin film in the presence of transverse fields, both at the surface, and within the bulk of the film, is investigated. The method adopted makes use of an effective field theory that includes the single-site spin correlations. Surface exchange enhancement within the surface and between the surface and the nearest-neighboring layer is accounted for. An expression for the critical ratio of the exchange couplings that lead to a Curie temperature higher than that for the infinite bulk material is obtained. This value is independent of the number of layers, L, in the film. It is shown that the surface and bulk transverse fields act in opposite ways on this critical ratio of the exchange couplings, with the result that in the presence of a uniform field the critical ratio is practically insensitive to the field strength. The dependence of the critical temperature on the thickness of the film is examined, and the reason for the conflicting results that have recently appeared in the literature for the zero field case resolved. The magnetic field dependence of the critical temperature is studied and the phase diagram in the (hs, hb, Js/Jb) space presented. (hs, Js and hb, Jb are the transverse field and the exchange coupling for the surface layer and the bulk of the film, respectively.) In the limit that L→∞, contact with previously reported results obtained for a semi-infinite slab is made.