HYPOTHESIS: Interfacial solvation forces arise from the organisation of liquid molecules near solid surfaces. They are crucial to fundamental phenomena, spanning materials science, molecular biology, and technological applications, yet their molecular details remain poorly understood. Achieving a complete understanding requires imaging techniques, such as three-dimensional atomic force microscopy (3D AFM), to provide atomically resolved images of solid-liquid interfaces (SLIs). However, converting 3D AFM data into accurate tip-sample forces remains challenging, as the process of translating observables into forces is not straightforward. EXPERIMENTS/SIMULATIONS: This study compares standard amplitude modulation AFM (AM-AFM) force reconstruction methods (FRMs) and identifies their limitations in reconstructing SLI forces. A novel numerical matrix-based FRM specifically designed for AM-AFM is then introduced, aiming to overcome the limitations and inaccuracies found in standard approaches. The new method is validated through simulations and experimental data obtained at the SLI of silicon oxide and water with 3D AFM. FINDINGS: The proposed matrix-based FRM, differently from standard FRMs, can reconstruct the full SLI interaction at the atomic scale, with no loss of information deriving from the specific choice of AFM experimental parameters or the force functional form. This method unlocks the full spectrum of physical phenomena encoded in the tip-sample interaction at the SLI in AFM experiments, greatly advancing our understanding of interfacial properties and their effects on colloid science, including nanoparticle interactions and molecular self-assembly.