A large fraction of exoplanets orbit within ∼1 au of their parent star suggesting either the formation at larger radii and planet migration towards shorter orbits or the in-situ formation at the current orbit. In both scenarios, our knowledge about planet formation and planet-disk interaction is limited by the predictions of disk models necessitating observational constraints of the physical conditions of the inner disk within Earth-like orbits. In this work, we use the CO overtone emission as a bonafide disk tracer to probe the innermost disk conditions. For the first time, we combine simultaneous optical interferometry using GRAVITY (UTs) and high-resolution CRIRES+ spectra. The combination of spectro-interferometric and high spectral resolution observations has allowed us to locate the CO emission and derive the temperature, column density, and kinematics of the CO-emitting gas for a sample of 4 intermediate-mass Herbig Ae/Be stars. Our results reveal that for all targets the CO is emitted from gas in Keplerian rotation within the dust sublimation front, that is, within the dust-free disk. Furthermore, we infer that the CO emitting gas is warm (∼2000K) and dense (∼1e21 cm−2). Finally, in order to reproduce our CRIRES+ spectra, broad local line widths are required which significantly exceed pure thermal broadening. These results show the potential of combining high resolution spectroscopy and interferometry to constrain the degree of turbulence in the inner disk.