The 10 year visiting VISA does not allow him to stay 10 years...he will still be subject to a restricted period of stay for each visit. This should have been noted in his I-94 when he arrived. You did not mention if he has overstayed that original period of time, but I wanted to bring it up, because if he has overstayed, and leaves the county, he may be subject to a ban from returning.
If he has overstayed, your best option would to marry him in the US ASAP and start the process to adjust his status to permanant resident.
If he has NOT overstayed, you have a few options.
First, like above stay in US marry him and adjust the status to LPR.
Second, let him go back to his country. From there, you could either file for a fiance VISA, have him come to the US and marry or you go to his country, marry, and apply for a spouse VISA. Either one of these you will still have to adjust his status
*** You mentioned he has to return to renew his Passport. Check with his countries Closest Embassy here in the US. They may be able to renew his passport here in the US. He must be in a legal status, not overstayed or anything. ***
A guess on the cost...forms could be around $1500-$3000. If you hire a lawyer (recommended), another $1500-$3000..depending on if there are any complications we do not know about. Also, part of the process is an affidavit of support that shows you or someone has enough money to support him, and is willing to take responsibility.
Here is a link to the immigration website where you can find more infromation.
http://www.uscis.gov/portal/site/uscis

