If you cannot get out of paying the tax, (Very important see below) you both should report the full 1099 amounts on your returns and then have a reconciling amount underneath that backs out the others half. I would also include their social security number and a brief explanation on this line so it makes it easier for the IRS to track. Before you do this on either of your returns, I would do the following:
You may want to take a look at the insolvency rules on Form 982 and the See link below:
Also, there are new rules out for deferring recognition of the debt forgiveness. See link below:
IRS Publication 4681Canceled Debts,Foreclosures, Repossessions, and Abandonments
These are all helpful links and sometimes the forms can be somewhat cumbersome. However, as you already know the tax on $139,000 is a very large number. Please take the time to understand the rules or pay somebody that will diligently go through the steps to protect your money.
If you have any questions, please do not hesitate to contact me.