The process in which a solute is transported across a lipid bilayer, from one side of a membrane to the other.
Comment
Transmembrane transport is the transport of a solute across a lipid bilayer. Note that transport through the nuclear pore complex is not transmembrane because the nuclear membrane is a double membrane and is not traversed. For transport through the nuclear pore, consider instead the term 'nucleocytoplasmic transport ; GO:0006913' and its children. Note also that this term is not intended for use in annotating lateral movement within membranes.