Lanthanide transition metal oxide hydride phases, LnSrCoO(3+alpha)RH(beta) (Ln) Pr, Nd), with variable H and O content, have been prepared by topotactic reduction of the parent n = 1 Ruddlesden-Popper phase, LnSrCoO(4), with CaH2 via a LnSrCoO(3.5) (Co2+) intermediate. The hydride anions occupy the site bridging the cations along the shorter in-plane direction in the CoOH plane. Substitution of oxide for hydride anions is incomplete leading to the compositions NdSrCoO3.084(4)H0.796(3) ( A), NdSrCoO3.210(3)H0.580(6) (B), and PrSrCoO3.160(4) H-0.680(7) (E) as determined by Rietveld refinement using powder neutron diffraction data. Diffraction, thermal gravimetry, and X-ray absorption spectroscopy show that the Co oxidation state remains close to +2 despite variation in hydride content. Variable temperature neutron powder diffraction studies show that the lanthanide size and H content strongly influence the Neel temperature (410 K ( A), 375 K (B), and 445 K (E)). All the materials are antiferromagnets. Magnetic short-range order (SRO) has also been observed, in the case of NdSrCoO3.210(3) H0.580(6) (B) the SRO is two-dimensional and persists above 440 K. Correlation lengths of similar to 100 angstrom indicate strong in-plane exchange interactions in the CoOH layers.