The nuclear-magnetic interference in the critical small-angle scattering of polarized neutrons from invar Fe₆₅Ni₃₅ near T_c = 485 K was investigated. The interference caused by the spin-lattice coupling revealed the correlation between critical fluctuations of magnetization and fluctuations of the nuclear density. The magnetic scattering allowed one to unambiguously identify a shape of the scattering objects as one of the critical fluctuation. The q-dependence of the interference scattering revealed that the shape of the scattering nuclear objects is essentially the same as the magnetic one. Therefore, the shape and lifetime of the scattering nuclear object are correlated with and terminated by that of the magnetic fluctuation. It was found that the expansion of the lattice is (δa/a) ≈ 0.004. The range of this expansion is of order 50 Å and depends on the temperature and magnetic field.