I'm writing a detective story set in the prohibition era. What do you think of my main characters?

Your characters sound suited to their parts and it sounds like you know them well enough to flesh them out nicely. Once concern, however, is the lady detective; in the Prohibition Era, this just didn't happen. Best to make her a wannabe--maybe the best one around, but she can't be officially a detective. This will be an element that can provide a lot of tension for your story. :) (If you're not sure what tension is in a story and why you need loads of it, google it--it's really important.)