The first measurement of lepton-jet momentum imbalance and azimuthal correlation in lepton-proton scattering at high momentum transfer is presented. These data, taken with the H1 detector at HERA, are corrected for detector effects using an unbinned machine learning algorithm (multifold), which considers eight observables simultaneously in this first application. The unfolded cross sections are compared with calculations performed within the context of collinear or transverse-momentum-dependent factorization in quantum chromodynamics as well as Monte Carlo event generators.