Great question. Turns out, there is some information about it.
For example, consider following resource: Membrane Protein Lipid Composition Atlas. Published by University of Michigan, it provides information on, primarily, protein content of different membranes from different species, but also has a list of lipid content.
Just as an example, consider following difference between membranes of mitochondria in yeast:
Now, concerning your interest in biophysics. To my taste, starting with just bulk lipid composition is a good first approximation. Although you also want to know about lipid raft formation and density/distribution of proteins. Next step, probably, will be symmetry considerations, that is, difference between sides of same membrane. You can imagine membranes with same bulk composition, but because of different lipid position (in/out) properties will be different.
It seems you can assess raft composition based on membrane lipid composition. Membrane capacity also is a property of membrane content.
Following quick walk through this Google Scholar search provides even more links between biophysical properties and lipid bilayer composition. However, it might be challenging to find exactly what you are looking for.