Context: Deep photometry of crowded fields, such as Galactic globular clusters, is severely limited by the resolution of ground-based telescopes. On the other hand, the Hubble Space Telescope does not have the near-infrared (NIR) filters needed to allow large color baselines. Aims: In this work we demonstrate how ground based observations can reach the required resolution when using Multi-Conjugated Adaptive Optic (MCAO) devices in the NIR, such as the experimental infrared camera (MAD) available on the VLT. This is particularly important since these corrections are planned to be available on all ground-based telescopes in the near future. Methods: We demonstrate this by combining the infrared photometry obtained by MAD/VLT with ACS/HST optical photometry of our scientific target, the bulge globular cluster NGC 6388, in which we imaged two fields. In particular, we constructed color-magnitude diagrams with an extremely wide color baseline in order to investigate the presence of multiple stellar populations in this cluster. Results: From the analysis of the external field, observed with better seeing conditions, we derived the deepest optical-NIR CMD of NGC 6388 to date. The high-precision photometry reveals that two distinct sub-giant branches are clearly present in this cluster. We also use the CMD from the central region to estimate the distance [ (m-M)_̂=15.33] and the reddening (E(B-V)=0.38) for this cluster. We estimate the age to be (~11.5± 1.5 Gyr). The large relative-age error reflects the bimodal distribution of the SGB stars. Conclusions: This study clearly demonstrates how MCAO correction in the NIR bands implemented on ground based telescopes can complement the high-resolution optical data from HST. Based on observations collected at the European Southern Observatory, Chile, as part of MAD Guaranteed Time Observations, and on NASA/ESA Hubble Space Telescope observations (GO-10775).