THE recent discovery of superconductivity in a number of alloys containing boron and carbon has revived interest in the field of intermetallic superconductors(1-3). Although two structural forms have now been identified(4-6), most of the new intermetallic superconductors have a crystal structure typified by that of the quaternary alloy LuNi2B2C, in which layers of rock-salt-structured LuC alternate with nickel boride tetrahedra(4,5). The range of superconducting intermetallic compounds was extended recently by the discovery of superconductivity in a system of quaternary boro-nitride alloys, La-Ni-B-N (ref. 7). Here we report the structure of the superconducting phase in this system, La3Ni2B2N3, together with that of the related non-superconducting phase, LaNiBN. We find that these two phases are members of a homologous series (LaN)(n)(Ni2B2), with n = 3 and n = 2, respectively. Furthermore, our samples contain planar defects that suggest the existence of phases with larger n. Varying the number, n, of LaN layers within this system might thus provide a way to investigate the effect of dimensionality on the superconducting properties of intermetallics.