An improved coating and spacer material for a medical device having a blood or tissue-contacting surface comprising a polyalkyleneimine layer which is crosslinked with a crosslinking agent which is at least difunctional in polymerizable vinyl groups which have adjacent strong electron-withdrawing groups and a biomolecule covalently bonded to the crosslinked polyalkyleneimine layer. For example, polyethyleneimine crosslinked with divinyl sulfone could be used. The resulting crosslinked spacer layer has improved uniformity and stability without materially limiting the covalent attachment of a biomolecule such as heparin.