The answer to this really depends on your working arrangement with your client and your friend.
The temptation is really to rewrite it and also put forth a few rules for your friend to work to in setting out and structuring their HTML.
If you and your friend are working together for the client then you can't really go to the client and admit that you need more money due to the mess that your friend had made.
At best you would have to get them to agree to the work on some other pretext - such as compliance with some new standards or to allow for inclusion on some new technology or even to allow for easier expansion later - anything but "we mucked up and need more money to correct it".
At worst you'll have to take the hit and do the work.
If your friend had produced this some time ago and you are working separately then you could try to get more money, by admitting that your initial estimate was incorrect.
I would just do what changes have minimal impact on your time, but allow you to implement the changes necessary.
This is usually the case with legacy software anyway.
Just remember next time to factor in a little leeway to allow for this type of thing when estimating work.