In order to enhance the scientific exploitation of adaptive optics (AO)-assisted observations, we investigate a novel hybrid concept to improve the parametric estimation of point spread function (PSF) called PSF Reconstruction and Identification for Multiple-source characterization Enhancement (PRIME). PRIME uses both focal and pupil-plane measurements to estimate jointly the model parameters related to the atmosphere [C2n(h)⁠, seeing] and the AO system (e.g. optical gains and residual low-order errors). Photometry and astrometry are provided as by-products. The parametric model in use is flexible enough to be scaled with field location and wavelength, making it a proper choice for optimized on-axis and off-axis data-reduction across the spectrum. Here, we present the methodology and validate PRIME on engineering and binary Keck II telescope NIRC2 images. We also present applications of PSF model parameters retrieval using PRIME: (i) calibrate the PSF model for observations void of stars on the acquired images, i.e. optimize the PSF reconstruction process, (ii) update the AO error breakdown mutually constrained by the telemetry and the images in order to speculate on the origin of the missing error terms and evaluate their magnitude, and (iii) measure photometry and astrometry with an application to the triple system Gl569 images.