We investigate inelastic cotunneling in a model system where the charging island is connected to the leads through molecules with energy-dependent transmission functions. To study this problem, we propose two different approaches. The first is a pragmatic approach that assumes Lorentzian-like transmission functions that determine the transmission probability to the island. Using this model, we calculate current versus voltage (IV) curves for increasing resonance level positions of the molecule. We find that shifting the resonance energy of the molecule away from the Fermi energy of the contacts leads to a decreased current at low bias, but as bias increases, this difference decreases and eventually inverses. This is markedly different from IV behavior outside the cotunneling regime. The second approach involves multiple cotunneling where also the molecules are considered to be in the Coulomb blockade regime. We find here that when Ec≫eV,kBT, the IV behavior approaches the original cotunneling behavior proposed by Averin and Nazarov [Phys. Rev. Lett. 65, 2446-2449 (1990)].