Disc-halo models of the Galaxy and Large Magellanic Cloud are constructed and used to analyse the microlensing data set. Deflectors in the LMC bar, disc and halo provide an optical depth to microlensing of ∼2 10−7. Deflectors in the Galactic disc and halo contribute ∼ 5 × 10−7. The extent, flattening and velocity anisotropy of the dark objects in the Galactic halo are unknown, so it is crucial to analyse the microlensing data set with families of models that span the viable ranges of these structural parameters. Also uncertain is the contribution of the Galactic disc to the local circular speed, which affects the normalization and size of the Galactic halo. Despite all the unknowns, a robust conclusion is that the Galactic and LMC haloes cannot be primarily built from objects in the mass range 10−7–0.1 M⊙. By contrast, calculations of the baryon mass fraction of the Galactic and LMC haloes are very sensitive to details of the adopted models. This parameter is not constrained by the existing data set. In particular, it is still possible for the halo to be entirely baryonic and composed of high-mass compact objects, like 104-M⊙ clusters.