Let me know if this is correct...
The more bright a solution, the greater absorbance, and hence the lower the transmittance????
You may be packing more into this question than you are aware of. Start with the definitions of each phenomenon, and then look at the system. You mention “chemiluminescence”, which is a particular mechanism for generating light energy. The things you mention can also take place in gases, liquids and solids! With respect to light:
Brightness - the subjective visual sensation related to the intensity of light emanating from a surface or from a point source. This may be emitted (generated) light or reflected light (albedo).
Absorbance- light waves are retained (absorbed) by the material through with they pass or impact.
Transmittance of light - light waves move all the way through a material without being absorbed or reflected
These parameters and definitions apply no matter where or how the light source originates. You can see that absorbance and transmission are related – essentially inverses of each other if there is no reflection. Brightness is a function of the available light energy, which will be affected by passing through a material.
The brightness of a particular chemiluminescent compound in solution would depend primarily on the concentration of the compound in solution. How bright it appears to the eye on leaving the solution may also depend on the solute and container materials. You generalization is incorrect. It is correct that transmission and absorbance are inverses, so a higher absorbance means that there is less transmission. However, neither of those affects the inherent brightness of a reaction taking place in or behind a particular material.
A “bright” solution would need a particular quantity (concentration) of the luminescing material with a minimum of absorbance, and maximum transmittance. Generally, higher concentrations would result in brighter emissions from the solution.
I'd like to add to Mr. Cooke's response. It is important to remember the Absorbance is defined as A= - log(T) where T is transmittance defined as I/Io. I and Io are defined as light intensity leaving and entering the sample, respectively.
In chemiluminescence, light is generated from within a sample via a chemical reaction. Therefore, Io is generated from within and not from an external source, like in most absorbance experiments. Because Io doesn't have a clear value, as it depends on concentration, kinetics, etc., it is hard to analytically use absorbance and transmittance in the context of chemiluminescence, which is further muddled by factors mentioned by Mr. Cooke.
I would also like to add on to Steven's excellent answer to emphasize a point he made:
"Brightness - the subjective visual sensation related to the intensity of light emanating from a surface or from a point source. "
Note the "subjective" in his statement. Wikipedia has a good article on the "brightness" as it relates to the measurement and description of color and color perception. Brightness is more used in descriptions of human perception of light and color than in technical measurements of say a chemiluminescent reaction which would usually be described in terms of measured light intensity (measured objectively by light meter).
It would be more correct to be using the term "intensity" (meaning a certain quantity of photons) which can be objectively measured rather than "brightness". This relates directly to the point Steven made- that the chemiluminescent intensity is dependent on the concentration of the reactants where a single reaction should produce a single photon so the number of photons (intensity) produced depends on the number of molecules reacting. If the light photons can be transmitted out of the container (because the energy was not absorbed by the molecules of the solute and the container) then how bright it would be would depend on your perception. Think of two situations: the same exact reaction set up - same concentration of reactants, same size and type of container, same solute - but running it once in ordinary room light and once in a dark room. If you have the same amount of reactants they will produce the same number of photons, but you will perceive it to be "brighter" in the dark room where it is the main source of light because your brain is now comparing that number of photons to darkness rather than comparing it to the room lights. The intensity (number of photons) is exactly the same in both cases but your perception of the light has changed. Therefore the importance of the word "subjective" in the definition of brightness. Brightness and transmission are related but not necessarily mathematically related to each other.
Note also that absorption is not "absorbance". As Greg pointed out, "absorbance" is a specific calculation based on transmittance which itself is a ratio of the light intensity passing through the sample to the light intensity shined on the sample. Absorption is just the physical process of light energy being added to the energy of a molecule. Transmission is also not "transmittance". Transmission is the physical process of light passing through the sample. The "transmittance" is a specific mathematical ratio comparing the light intensity coming out of a sample to light intensity shining on the sample (going in). So you can talk about the light being transmitted and absorbed in a container with a chemiluminescent reaction but that is not the same as absorbance and transmittance.
Sorry to be so picky about the terms but they have specific meanings in chemistry/physics that are important to the technical understanding.