SUMMARY Satellite observations of the geomagnetic field contain signals generated in Earth’s interior by electrical currents in the core and by magnetized rocks in the lithosphere. At short wavelengths the lithospheric signal dominates, obscuring the signal from the core. Here we present details of a method to co-estimate separate models for the core and lithospheric fields, which are allowed to overlap in spherical harmonic degree, that makes use of prior information to aid the separation. Using a maximum entropy method we estimate probabilistic models for the time-dependent core field and the static lithospheric field that satisfy constraints provided by satellite observations while being consistent with prior knowledge of the spatial covariance and expected magnitude of each field at its source surface. For the core field, we find that between spherical harmonic degree 13 and 22 power adds coherently to the established structures, and present a synthetic test that illustrates the aspects of the small scale core field that can reliably be retrieved. For the large scale lithospheric field we also find encouraging results, with the strongest signatures below spherical harmonic degree 13 occurring at locations of known prominent lithospheric field anomalies in the northern part of Eastern Europe, Australia and eastern North America. Although the amplitudes of the small scale core field and large scale lithospheric field are likely underestimated we find no evidence that obvious artefacts are introduced. Compared with conventional maps of the core–mantle boundary field our results suggest more localized normal flux concentrations close to the tangent cylinder, and that low latitude flux concentrations occur in pairs with opposite polarities. Future improvements in the recovery of the small scale core field and large scale lithospheric field will depend on whether more detailed prior information can be reliably extracted from core dynamo and lithospheric magnetization simulations.