All radiation is thermal. I really can´t understand why anyone makes a difference between different parts of the spectrum. The "visual" part of radiation is entirely relative to human eye-sight. The definition of visual is exactly that, the radiation which the receptors in our eyes respond to. The concept "albedo" is also something entirely relative to human eye-sight, and it should be questioned if it is correct to use it for a planet in regards to temperature at all. For example, snow is like a perfect blackbody absorber outside the visual spectrum, but in the visual it is reflective. And solar radiation is 51% IR(thermal), so what use do we have of "albedo" when we calculate temperature?
"Thermal" radiation is entirely based on the fact that human eyes doesn´t respond to those wavelengths, and the rest of the longwave radiation parts of the spectrum is called non-thermal mostly because humans can´t sense it at all.
"Solar radiation" cover the spectral parts where we say that the gases in question is opaque, although wavelengths are mostly in the higher frequency part. So the "transparent" parts apply to both solar and thermal, with your definitions.
The fact is, all radiation is thermal, intensity and wavelengths depends on the temperature of the emitter, only. Any part of the spectrum has an intensity according to the temperature of the emitter, spectral resolution and peak intensity of emission is also caused by the temperature of the emitter. The entire concept of radiation in the universe is an exclusive relationship where emission depends on temperature alone. If we know this, which we do, then all radiation is thermal. And nothing on earth, no matter what gases are involved, should interfere with that relationship, because it would be a violation of 100% consensus physics. Emission is dependent on temperature alone, absorption is due to temperature only. Spectral resolution is quantum physics, and we don´t use that for temperature. Now, if you want to discuss spectral character of something, that is fine. But if we are talking about temperature, of the atmosphere or earth surface, transparency should not be involved.