I guess it depends on the type of properties you are interested in. If you are interested in lipid dynamics, the usual techniques are Fluorescence correlation spectroscopy (FCS) and Fluorescence Lifetime Imaging Microscopy (FLIM). These techniques can be used in the Total Internal Reflection Fluorescence (TIRF) mode to study membrane properties near cell focal adhesions.
We have extensively studied biological membranes(chloroplasts, thylakoids) and bilayer, micellar and hexagonal phase aqueous lipid dispersions as well as intact bacterial membrane structural and physiological aspects using transmission electron microscopy besides lipid dynamics by maganetic resonance spectroscopy. May see these publications at my ResearchGate page.
The transmission electron microscope is definitely ideal.
The scanning electron microscope remains a good substitute, for example I have a Zeiss EVO LS10 where I mounted the STEM detector that allows me to use the same transmission grids and have immaqgini fully comparable with the transmission.
It depends on the spatial resolution: AFM or electron micrsocopy for nm, SEM for nm-microns, optical for less resolution.
Cryotechniques (freeze fracture or Cryomicroscopy) use freezing to preserve structures. FFEM offers a topological view of surfaces (it's transmission but you 'make' a metallic replica of the sample); Cryo-TEM requires low concentrations of sample.