This happened to our former nanny when we did a share! The problem is that neither employer takes out enough taxes because your tax rate/bracket is calculated separately for each family. So the payroll software calculates your tax withholding based on the wrong tax bracket (too low!). Basically, you are being taxed each paycheck as if your annual salary was only half of what it really is. Then when tax season rolls around, you owe.
To fix this next year, you should have each employer withhold an extra amount each pay period. Or see if the W4 has a calculator to help you figure out what to do for more than one job. For tax withholding purposes, you have two separate jobs.