The structures that pass between middle cerebellar peduncle and pons is
Trigeminal nerve exits the brain by a large sensory root and a smaller motor root coming out of the pons at its junction with the middle cerebral peduncle.(Ref: Vishram Singh textbook of clinical neuroanatomy second edition pg-81, fig 8.9)
Trigeminal nerve
Vagus nerve
Olfactory nerve
Optic nerve
Brain 