Despite the ever-growing number of ocean data, the interior of the ocean remains undersampled in regions of high variability such as the Gulf Stream. In this context, neural networks have been shown to be effective for interpolating properties and understanding ocean processes. We introduce OSnet (Ocean Stratification network), a new ocean reconstruction system aimed at providing a physically consistent analysis of the upper ocean stratification. The proposed scheme is a bootstrapped multilayer perceptron trained to predict simultaneously temperature and salinity (T−S) profiles down to 1000 m and the mixed-layer depth (MLD) from surface data covering 1993 to 2019. OSnet is trained to fit sea surface temperature and sea level anomalies onto all historical in situ profiles in the Gulf Stream region. To achieve vertical coherence of the profiles, the MLD prediction is used to adjust a posteriori the vertical gradients of predicted T−S profiles, thus increasing the accuracy of the solution and removing vertical density inversions. The prediction is generalized on a 1/4∘ daily grid, producing four-dimensional fields of temperature and salinity, with their associated confidence interval issued from the bootstrap. OSnet profiles have root mean square error comparable with the observation-based Armor3D weekly product and the physics-based ocean reanalysis Glorys12. The lowest confidence in the prediction is located north of the Gulf Stream, between the shelf and the current, where the thermohaline variability is large. The OSnet reconstructed field is coherent even in the pre-Argo years, demonstrating the good generalization properties of the network. It reproduces the warming trend of surface temperature, the seasonal cycle of surface salinity and mesoscale structures of temperature, salinity and MLD. While OSnet delivers an accurate interpolation of the ocean stratification, it is also a tool to study how the ocean stratification relates to surface data. We can compute the relative importance of each input for each T−S prediction and analyse how the network learns which surface feature influences most which property and at which depth. Our results demonstrate the potential of machine learning methods to improve predictions of ocean interior properties from observations of the ocean surface.