We provide a theoretical frame for in situ scanning tunneling microscopy (STM) of adsorbate molecules with low-lying redox levels strongly coupled to the environmental nuclear motion. The STM process is viewed as a coherent two-step electron transfer (ET) involving electron exchange between the local redox level and the manifolds of electronic levels in the substrate and tip. The notion coherence is here taken to imply that the intermediate electron or hole state after the first ET step does not fully relax vibrationally before the second ET step. These views and the theoretical formalism are appropriate to in situ STM of large transition metal complexes and redox metalloproteins. The formalism offers two kinds of spectroscopic features. One is the relation between the tunnel current and the bias voltage at fixed overvoltage of either the tip or the substrate relative to a reference electrode. The other one is the tunnel current dependence on the overvoltage, at fixed bias voltage. Recent data on tunneling current patterns for adsorbed or covalently tethered metalloporphyrins and the blue single-copper protein azurin are discussed in terms of the formalism.