Block copolymer amphiphiles that self-assemble into membranes present robust and functionalizable alternatives to biological assemblies. Coarse-grained molecular dynamics shows that thick bilayers of A-B copolymers accommodate protein-like channels and also tend to regulate transport. This occurs as flexible, hydrophilic A chains insert into the pore and obstruct water entry. A-B-A triblocks that exploit "hairpin" and "straight" conformations also show assembly into novel nanotubules and further highlight the key roles for chain flexibility in biomimetic block copolymer assemblies.