There are a few things to clarify, this is a more QM answer:
You are asking about visible wavelength photons, so I am going to talk about those.
When the photons in your case interact with the glass lattice atoms, there is:
elastic scattering, the photons keep their energy and phase
inelastic scattering, the photons keep part of their energy and phase
absorption, the photons give all their energy to the atom
Now when the photons interact with the glass, all three happen, but their ratio is different.
In the case of glass, there is:
reflection, that is the mirror image of yourself, that is 1., elastic scattering, the photons keep their absolute energy and phase and relative energy and phase and angle, this is the only way to build an almost perfect mirror image. It is very important to understand that even with reflection, all three happens, but most of the photons get elastically scattered, and the ratio of inelastic scattering and absorption is very little.
refraction, that is the image that goes through the glass, that is 1. too, elastic scattering, the photons keep their absolute energy, phase, and relative energy and phase and angle, this is the only way to keep an almost perfect image through the glass. It is very important to understand that with refraction, all three happen, most of the photons get elastically scattered, and the inelastically scattered and absorbed photons' ratio is very little.
absorption, that is 3., when the photons' energy gets transferred into the vibrational energies of the glass lattice molecules, heats up the metal.
Now it is as per QM all about probabilities, but when the photons (visible wavelength) reach the first glass, 4% will be reflected, and 96% will be refracted.
What is the difference between them? The angle only. Both reflected and refracted will be elastically scattered. On this site, there is a debate whether refraction is elastic scattering or absorption and re-emission. Now it is elastic scattering. That is the only way to keep the photons' absolute energy, phase and relative energy, phase and angle. This is the only way to keep a mirror image through the glass.
So both the reflected and refracted photons get elastically scattered, 4% of them will change angle almost backwards, and 96% forwards relative to the angle of incidence. So the only difference is the angle. Why? It is the lattice structure of glass. It has a 4-96 ratio of probabilities of photons' interference (for visible wavelength) being constructive backwards (reflection) or forwards (refraction) angle. Metal has a 99-0 (for visible wavelength) ratio of probabilities of photons' interference being constructive backwards or forwards.
Now in your case, the first glass will reflect 4% of the photons, 96% will go through. The 4% will be visible for you as tour own mirror image. The 96% will go through, and at the second glass, 0.96*96% will go through, and 0.04*96% will be reflected. So when the 0.04*96% reaches the first glass backwards, 0.04*0.04*96% will be reflected backwards as a mirror image. And 0.96*0.04*96% will go through the first glass backwards, and you will see those as your own reflection too.