Virtual-pinhole PET (VP-PET) imaging is a new technology in which one or more high-resolution detector modules are integrated into a conventional PET scanner with lower resolution detectors. It can locally enhance the spatial resolution and contrast recovery near the add-on detectors, and depending on the configuration, may also increase the sensitivity of the system. This novel scanner geometry makes the reconstruction problem more challenging compared to the reconstruction of data from a stand-alone PET scanner, as new techniques are needed to model and account for the non-standard acquisition. In this paper, we present a general framework for fully 3D modeling of an arbitrary VP-PET insert system. The model components are incorporated into a statistical reconstruction algorithm to estimate an image from the multi-resolution data. For validation, we apply the proposed model and reconstruction approach to one of our custom-built VP-PET systemsa half-ring insert device integrated into a clinical PET/CT scanner. Details regarding the most important implementation issues are provided. We show that the proposed data model is consistent with the measured data, and that our approach can lead to reconstructions with improved spatial resolution and lesion detectability.