Yes because Vicodin has hydrocodone/tylenol....naproxen is an anti inflammatory medication. They are from two separate families of medication and are safe to take together. The biggest problem with this is that the vicodin can be upsetting to the stomach as well as the naproxen. Stomach and gastrointestinal upset is a possible side effect.
Hydromorphone does not have acetaminophen or Tylenol and Vicodin does. Some people take Hydromorphone for all day pain relief and the Vicodin for break-thru pain. You cannot mix any medication that has acetaminophen with Vicodin or anything that has acetaminophen in it, and should always take drugs only under a doctor's care.