The entanglement properties of two initially coherent electromagnetic-field modes copropagating through a lossless nonlinear medium are investigated. Disentangled states are observed to occur periodically. By taking a suitable set of nonlinear parameters, these states become a macroscopically well-distinguishable coherent superposition. Between two consecutive disentanglements the modes reach partial disentanglements, with the purity measure evolving into a multifractal measure for large mean photon number. Following standard statistical techniques, the singularity spectrum of the purity measure is obtained to characterize its universal scaling properties.