Poor dispersibility in aqueous media of polymer functionalized one-dimensional materials including carbon nanotubes (CNTs), inorganic nanoparticles and polymer nanofibers is an inherent challenge to their utilization in several applications. Herein, polydopamine grafted CNTs (PDA-CNTs) are rendered dispersible through chemical crosslinking via bioinspired borate chemistry. Nanolayer coatings of polydopamine are deposited on the side walls of CNTs forming aggregates that lead to highly dense and agglomerated PDA-CNTs sediments in aqueous media. Borate crosslinking facilitates the obtainment of a homogeneous dispersion of borate crosslinked PDA-CNTs (B-PDA-CNTs) by forming strong hydrogen bonds in solution and thus permitting the facile fabrication of B-PDA-CNTs membranes with an interconnected nanoporous structure on a macroporous support. The obtained membranes with a controllable thickness are stable and display good ultrafiltration performances of ferritin molecules (> 90%) and high water permeability of more than 2.8x10(3)Lm(-2) h(-1) bar(-1). The borate chemical crosslinking highlights a versatile approach for the preparation of stable polydopamine coated nanomaterials for wide applications with bio-macromolecules and in nanocomposite materials.