Is it possible to have sleep apnea and insomnia?

Apnea + insomnia-yes: Sleep apnea and insomnia are 2 separate diagnoses, and can be present in the same person. With sleep apnea, a person stops breathing during sleep, usually due to mechanical obstruction of the airway by his own tissues. This happens after induction of sleep. Insomnia means trouble falling asleep or staying asleep. Sleep apnea can be a type of trouble staying asleep, but usually not falling asleep.

Yes: Actually, it has been shown that insomnia is present in about 25% of patients with obstructive sleep apnea. Once you treat the sleep apnea, insomnia generally improves.