First, figure out why you are being underpaid. Is it because you changed locations and didn't know the market, are you able to do a job more senior than the one you current have, etc? If it is something like that then once you get the offer, explain that. Explain how this job isn't a side step and you are underemployed, or whatever the case may be. Most of the times making an offer to a percentage of the candidates current salary is only a strict rule if it is a lateral move. If you can make the case that it isn't for whatever reason, then that rule should relax and you should be able to get yourself more money. Now wait until you have an offer though, or you may be talking yourself out of a job by making your current job sound less than what it really is.
Now if you have no good reason and you simply let the market pass you by while you weren't looking, it isn't as easy. The first step is to tell your boss what you now know. Even if they won't get you to where you want to be every bit helps, and until you leave it is still money. Even if you get a small raise this way you should still move on. Either your boss isn't aware enough to know you are underpaid, or is aware and is fine with it. I don't care which it is, you deserve a better boss. Now when you get an offer, be honest. Tell them you know you are being underpaid and this offer while more money is still less than you are worth. See what they say. If they say that is the policy and they can't give you too much more than you already make then ask if they will work to help get you to where you should be over the next two years or so. If you think about it, it really isn't a good idea for a company to underpay their employees, it just causes turnover. Managers really get together and call out who is underpaid and they give them bigger raises than normal to get them up to where they should be so they won't leave. Your best hope is to find a company that will do that. You won't get any of that in writing and the HR person won't like talking about that at all, talk to the hiring manager about it. If you can't get that, then you will have to hop two or three jobs to get where you should be. But once you are there be picky and find a good place and stay there for a long time. No one likes hiring someone who switches jobs every year. And try not to let yourself fall so far behind again.
Good luck, and feel free to keep the conversation going.