A new modification of PbF(IO3) has been obtained as single crystals from hydrothermal synthesis, alongside the known centrosymmetric, Pb(IO3)2, as a second phase. Measured with the Kurtz-Perry SHG method, the new crystals are phase-matchable for YAG:Nd laser radiation and demonstrate strong SHG output. According to an X-ray diffraction analysis conducted on a single crystal at low temperature, the new crystals appear monoclinic, of space group Pn, as opposed to the known orthorhombic modification of the PbF(IO3), of space group Iba2. The new crystals were also measured at room temperature, showing an orthorhombic disordered variant of the new phase (space group C2ma, standard Abm2). This variant presents an “average structure” with the mirror plane in the group. The low-temperature X-ray single-crystal experiment allowed us to find the correct structural model, where the mirror plane was found as a twin element in the real monoclinic Pn structure. A careful crystal chemical analysis led to a whole family of nonlinear optical crystals with a common formula, AX(IO3), A = Bi, Ba, Pb, X = O, F, (OH), currently counting six representatives, including the well-known BiO(IO3). All of them possess common central cationic layers similar to those known in Aurivillius-type phases, with anionic iodate layers attached above and below these layers instead of the perovskite-like, or halogens. The structure–property relationships are discussed with respect to the important role of the large cations: Pb2+, Bi3+ or Ba2+. A number of iodates with similar structures are also analyzed.