While the realistic modeling of the thermodynamic behavior of fluids usually demands elaborated atomistic models, much has been learned from simplified ones. Here, we investigate a model where pointlike particles (with activity z0) are mixed with molecules that exclude their first and second neighbors (i.e., cubes of lateral size λ=3a, with activity z2), both placed on the sites of a simple cubic lattice with parameter a. Only hard-core interactions exist among the particles so that the model is athermal. Despite its simplicity, the grand-canonical solution of this model on a Husimi lattice built with cubes revels a fluid-fluid demixing, yielding a phase diagram with two fluid phases (one of them dominated by small particles-F0) and a solidlike phase coexisting at a triple-point. Moreover, the fluid-fluid coexistence line ends at a critical point. An anomaly in the total density (ρT) of particles is also found, which is hallmarked by minima in the isobaric curves of ρT vs z0 (or z2). Interestingly, the line of minimum density crosses the phase diagram starting inside the region where both fluid phases are stable, passing through the F0 one and ending deep inside its metastable region, in a point where the spinodals of both fluid phases cross each other.