Yes, these drugs are opiate-based and therefore will show up in a urine drug screen as opioid positive result, hope this is useful to you.
Does Lortab Codeine And Oxycodone Show Up As A Opiate In Urine Drug Test?
Yes, I know for sure that Lortab and Oxycodone do. Not as sure about codeine, but probably cause it's a mild relative of morphine.