I disagree with the premise of this question. Using DC permittivity and DC resistivity is an awful starting point if you want to understand anything about visible-light response. [Update: I should say that it's not that bad a starting point for metals specifically. Much worse for other materials.] When electrons move back and forth at 60 Hz, they usually move in a totally different way than when they move back and forth at 1 quadrillion Hz.
For example, in an n-type semiconductor, at 60 Hz, the conductance comes from electrons in the conduction band getting shifted within the band and traveling and sometimes bumping into defects. The conductance at 1 quadrillion Hz comes from electrons in the valence band being pulled into a quantum superposition state between valence and conduction band states. The superposition state happens to jiggle back and forth (by atomic-scale distances) at 1 quadrillion Hz, because of the energy difference between the two states and the laws of quantum mechanics. Soon the superposition is disturbed and you get an electron-hole pair.
For example, rubber has a very high resistivity but is not transparent. Indium-tin-oxide has a low resistivity but is transparent.
To understand visible absorption, you need to be thinking about energy levels and modes, not DC resistivity.
Water absorbs visible light because of various weak (harmonic) vibrational modes. Normally, vibration modes are only in the infrared, but water has unusually high-frequency vibration modes that reach just a bit into the visible. (Because hydrogen is light and bonds very tightly to oxygen. Just like a taut thin string on a guitar will vibrate at a higher frequency than a loose thick string.) Glass does not have that property.
Glass can be much more transparent than water: For example, fiber optics are glass strands through which light can travel many kilometers with negligible absorption. Fiber optics are manufactured very carefully to reduce absorption; if you made ordinary window glass that was 1km thick, it would certainly be opaque.
Usage of the word "translucent" is inconsistent. Historically, according to the Oxford English Dictionary, until about the mid 18th century it simply meant transparent. More recently it is used in two different ways. Sometimes it is used as you suggest meaning semitransparent, allowing some light, but not all, to pass through. For example in the Wikipedia article on Opacity.
An opaque object is neither transparent (allowing all light to pass through) nor translucent (allowing some light to pass through).
I have seen also seen it defined this way in high school science texts. More often, at least by my judgement, the translucency of an object is describes the degree to which light is scattered as it passes through it. In this usage it is not directly related to transparency.
Gammarist.com explains the difference like so:
Things that are transparent are so clear you can see through them as if there’s nothing there. Things that are translucent allow light through but with significant diffusion or distortion.
The Wikipedia article on Transparency and Translucency says essentially the same thing but with more detail.
In other words, a translucent medium allows the transport of light while a transparent medium not only allows the transport of light but allows for image formation. The opposite property of translucency is opacity. Transparent materials appear clear, with the overall appearance of one color, or any combination leading up to a brilliant spectrum of every color.
If it were up to me translucent would only be used to describe substances that scatter light as it passes through but that's not the way everyone uses it.
Best Answer
Photons pass through glass because they are not absorbed. And they are not absorbed because there is nothing which "absorbs" light in visual frequencies in glass. You may have heard that ultraviolet photons are absorbed by glass, so glass is not transparent for them. Exactly the same happens with X-rays for which our body is nearly transparent whilst a metal plate absorbs it. This is experimental evidence.
Any photon has certain frequency - which for visible light is related to the colour of light, whilst for lower or upper frequencies in the electromagnetic spectrum it is simply a measure of the energy transported by photon. A material's absorption spectrum (which frequencies are absorbed and how much so) depends on the structure of the material at atomic scale. Absorption may be from atoms which absorb photons (remember - electrons go to upper energetic states by absorbing photons), from molecules, or from lattices. There are important differences in these absorption possibilities:
As glass is a non-crystalline, overcooled fluid, consisting of molecules, its absorption occurs in the 1st and 2nd ways, but because of the matter it is composed of, it absorbs outside our visible spectrum.