We investigate the problem of wetting transitions in polymer blends confined to a slitlike adsorbing capillary of thickness H by Monte Carlo methods. Two paths for capillary wetting are considered, either along a path of increasing temperature, T, or increasing surface chemical potential, mu(1). We find that H can be thought of as an additional thermodynamic parameter which controls the nature of the transitions. We find that there exists a capillary critical separation, H-c. For separations less than H-c the blend falls in the one phase region of the phase diagram. Above H-c there exists a separation H-bulk, where the polymer blend begins to show bulk behavior. H-bulk is shown to separate regions of first order transitions (H < H-bulk) from critical wetting transitions (H greater than or equal to H-bulk). Along a path of constant T and increasing mu(1) we find for 2 xi < H-1 < H-2 < H-bulk that the first-order transitions between the two separations is shifted according to mu(1)(c)(H-2) - mu(1)(c)(H-1) proportional to 1/H-1 - 1/H-2. We discuss the implications of these results for the case of H --> infinity and compare them with theoretical results.