We use neutron scattering to study the lattice and magnetic structure of the layered half-doped manganite Pr(0.5)Ca(1.5)MnO(4). On cooling from high temperature, the system first becomes charge-and orbital-ordered (CO/OO) near T(CO) = 300 K and then develops checkerboard-like antiferromagnetic (AF) order below T(N) = 130 K. At temperatures above T(N) but below T(CO) (T(N)<T<T(CO)), the appearance of short-range AF spin correlations suppresses the CO/OO-induced orthorhombic strain, contrasting with other half-doped manganites, where AF order has no observable effect on the lattice distortion. These results suggest that a strong spin-lattice coupling and the competition between AF exchange and CO/OO ordering ultimately determines the low-temperature properties of the system.