We report a Monte Carlo (MC) simulation study of a model discotic liquid crystal (DLC) confined between hybrid walls with controllable penetrability. The model consists of oblate hard Gaussian overlap (HGO) particles. Particle-substrate interactions are modeled as follows: each substrate sees a particle as a disc of zero thickness and diameter D less than or equal to that of the actual particle, sigma(0), embedded inside the particle and located halfway along, and perpendicular to, its minor axis. This allows us to control the anchoring properties of the substrates, from planar (edge-on) for D approximate to 0 to homeotropic (face-on) for D approximate to sigma(0), which can be done independently at either substrate. Depending on the values of D-s = D/sigma(0) at the top (D-s(t)) and bottom (D-s(b)) substrates, we find domains in (D-s(b), D-s(t)) space in which particle alignment is uniform planar (UP), is uniform homeotropic (UH), or varies linearly from planar at one substrate to homeotropic at the other (Lin). These domains are separated by regions of bistability (P-Lin and H-Lin), which appear to be wider than for prolate HGOs, and there may be also a small tristable (P-H-Lin) region. Results are compared with the predictions of density functional theory, implemented at the level of Onsager's second-virial approximation with Parsons-Lee rescaling. As in the case of symmetric confinement studied previously, the agreement between theory and simulation is substantially less good than for prolate HGOs: in particular, for the investigated substrate separation L = 6 sigma(0), the Lin configuration is never predicted. These discrepancies are likely a consequence of the fact that Onsager's theory is less accurate for discs than for rods.