We have studied the temperature dependence of the in-plane resistivity of NbN/AlN multilayer samples with varying insulating layer thickness in magnetic fields up to 7 Tesla parallel and perpendicular to the films. The upper critical field shows a crossover from 2D to 3D behavior in parallel fields. The irreversibility lines have the form (1-T/Tc)^alpha, where alpha varies from 4/3 to 2 with increasing anisotropy. The results are consistent with simultaneous melting and decoupling transitions for low anisotropy sample, and with melting of decoupled pancakes in the superconducting layers for higher anisotropy samples.
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